Practical number (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Practical number" in English language version.

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10doi.org

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6ams.org

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6semanticscholar.org

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6arxiv.org

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2web.archive.org

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1jstor.org

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1uwaterloo.ca

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1currentscience.ac.in

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1nju.edu.cn

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ams.org

mathscinet.ams.org

Margenstern (1991) cites Robinson (1979) and Heyworth (1980) for the name "panarithmic numbers". Margenstern, Maurice (1991), "Les nombres pratiques: théorie, observations et conjectures", Journal of Number Theory, 37 (1): 1–36, doi:10.1016/S0022-314X(05)80022-8, MR 1089787. Robinson, D. F. (1979), "Egyptian fractions via Greek number theory", New Zealand Math. Mag., 16 (2): 47–52. As cited by Margenstern (1991) and Mitrinović, Sándor & Crstici (1996). Heyworth, M. R. (1980), "More on panarithmic numbers", New Zealand Math. Mag., 17 (1): 24–28. As cited by Margenstern (1991).
Hausman & Shapiro (1984); Margenstern (1991); Melfi (1996); Saias (1997). Hausman, Miriam; Shapiro, Harold N. (1984), "On practical numbers", Communications on Pure and Applied Mathematics, 37 (5): 705–713, doi:10.1002/cpa.3160370507, MR 0752596. Margenstern, Maurice (1991), "Les nombres pratiques: théorie, observations et conjectures", Journal of Number Theory, 37 (1): 1–36, doi:10.1016/S0022-314X(05)80022-8, MR 1089787. Melfi, Giuseppe (1996), "On two conjectures about practical numbers", Journal of Number Theory, 56 (1): 205–210, doi:10.1006/jnth.1996.0012, MR 1370203. Saias, Eric (1997), "Entiers à diviseurs denses, I", Journal of Number Theory, 62 (1): 163–191, doi:10.1006/jnth.1997.2057, MR 1430008.
Stewart (1954); Sierpiński (1955). Stewart, B. M. (1954), "Sums of distinct divisors", American Journal of Mathematics, 76 (4), The Johns Hopkins University Press: 779–785, doi:10.2307/2372651, JSTOR 2372651, MR 0064800. Sierpiński, Wacław (1955), "Sur une propriété des nombres naturels", Annali di Matematica Pura ed Applicata, 39 (1): 69–74, doi:10.1007/BF02410762, S2CID 121592840.
Margenstern (1991). Margenstern, Maurice (1991), "Les nombres pratiques: théorie, observations et conjectures", Journal of Number Theory, 37 (1): 1–36, doi:10.1016/S0022-314X(05)80022-8, MR 1089787.
Srinivasan (1948). Srinivasan, A. K. (1948), "Practical numbers" (PDF), Current Science, 17: 179–180, MR 0027799, archived from the original (PDF) on 2016-03-05.
Melfi (1996). Melfi, Giuseppe (1996), "On two conjectures about practical numbers", Journal of Number Theory, 56 (1): 205–210, doi:10.1006/jnth.1996.0012, MR 1370203.

arxiv.org

Eppstein (2021). Eppstein, David (2021), "Egyptian fractions with denominators from sequences closed under doubling", Journal of Integer Sequences, 24: 21.8.8, arXiv:2109.12217
Weingartner (2022). Weingartner, A. (2022), "Somewhat smooth numbers in short intervals", Ramanujan Journal, 60 (2): 447–453, arXiv:2105.13568, doi:10.1007/s11139-022-00552-w, S2CID 235247868.
Weingartner (2015) and Remark 1 of Pomerance & Weingartner (2021) Weingartner, A. (2015), "Practical numbers and the distribution of divisors", The Quarterly Journal of Mathematics, 66 (2): 743–758, arXiv:1405.2585, doi:10.1093/qmath/hav006. Pomerance, C.; Weingartner, A. (2021), "On primes and practical numbers", Ramanujan Journal, 57 (3): 981–1000, arXiv:2007.11062, doi:10.1007/s11139-020-00354-y, S2CID 220686445.
Weingartner (2020). Weingartner, A. (2020), "The constant factor in the asymptotic for practical numbers", International Journal of Number Theory, 16 (3): 629–638, arXiv:1906.07819, doi:10.1142/S1793042120500311, S2CID 195069356.
Weingartner (2019). Weingartner, A. (2019), "On the constant factor in several related asymptotic estimates", Mathematics of Computation, 88 (318): 1883–1902, arXiv:1705.06349, doi:10.1090/mcom/3402, S2CID 85532616.
Weingartner (2021) Weingartner, A. (2021), "An extension of the Siegel-Walfisz theorem", Proceedings of the American Mathematical Society, 149 (11): 4699–4708, arXiv:2011.06627, doi:10.1090/proc/15607, S2CID 226956079.

currentscience.ac.in

Srinivasan (1948). Srinivasan, A. K. (1948), "Practical numbers" (PDF), Current Science, 17: 179–180, MR 0027799, archived from the original (PDF) on 2016-03-05.

doi.org

Margenstern (1991) cites Robinson (1979) and Heyworth (1980) for the name "panarithmic numbers". Margenstern, Maurice (1991), "Les nombres pratiques: théorie, observations et conjectures", Journal of Number Theory, 37 (1): 1–36, doi:10.1016/S0022-314X(05)80022-8, MR 1089787. Robinson, D. F. (1979), "Egyptian fractions via Greek number theory", New Zealand Math. Mag., 16 (2): 47–52. As cited by Margenstern (1991) and Mitrinović, Sándor & Crstici (1996). Heyworth, M. R. (1980), "More on panarithmic numbers", New Zealand Math. Mag., 17 (1): 24–28. As cited by Margenstern (1991).
Hausman & Shapiro (1984); Margenstern (1991); Melfi (1996); Saias (1997). Hausman, Miriam; Shapiro, Harold N. (1984), "On practical numbers", Communications on Pure and Applied Mathematics, 37 (5): 705–713, doi:10.1002/cpa.3160370507, MR 0752596. Margenstern, Maurice (1991), "Les nombres pratiques: théorie, observations et conjectures", Journal of Number Theory, 37 (1): 1–36, doi:10.1016/S0022-314X(05)80022-8, MR 1089787. Melfi, Giuseppe (1996), "On two conjectures about practical numbers", Journal of Number Theory, 56 (1): 205–210, doi:10.1006/jnth.1996.0012, MR 1370203. Saias, Eric (1997), "Entiers à diviseurs denses, I", Journal of Number Theory, 62 (1): 163–191, doi:10.1006/jnth.1997.2057, MR 1430008.
Stewart (1954); Sierpiński (1955). Stewart, B. M. (1954), "Sums of distinct divisors", American Journal of Mathematics, 76 (4), The Johns Hopkins University Press: 779–785, doi:10.2307/2372651, JSTOR 2372651, MR 0064800. Sierpiński, Wacław (1955), "Sur une propriété des nombres naturels", Annali di Matematica Pura ed Applicata, 39 (1): 69–74, doi:10.1007/BF02410762, S2CID 121592840.
Margenstern (1991). Margenstern, Maurice (1991), "Les nombres pratiques: théorie, observations et conjectures", Journal of Number Theory, 37 (1): 1–36, doi:10.1016/S0022-314X(05)80022-8, MR 1089787.
Melfi (1996). Melfi, Giuseppe (1996), "On two conjectures about practical numbers", Journal of Number Theory, 56 (1): 205–210, doi:10.1006/jnth.1996.0012, MR 1370203.
Weingartner (2022). Weingartner, A. (2022), "Somewhat smooth numbers in short intervals", Ramanujan Journal, 60 (2): 447–453, arXiv:2105.13568, doi:10.1007/s11139-022-00552-w, S2CID 235247868.
Weingartner (2015) and Remark 1 of Pomerance & Weingartner (2021) Weingartner, A. (2015), "Practical numbers and the distribution of divisors", The Quarterly Journal of Mathematics, 66 (2): 743–758, arXiv:1405.2585, doi:10.1093/qmath/hav006. Pomerance, C.; Weingartner, A. (2021), "On primes and practical numbers", Ramanujan Journal, 57 (3): 981–1000, arXiv:2007.11062, doi:10.1007/s11139-020-00354-y, S2CID 220686445.
Weingartner (2020). Weingartner, A. (2020), "The constant factor in the asymptotic for practical numbers", International Journal of Number Theory, 16 (3): 629–638, arXiv:1906.07819, doi:10.1142/S1793042120500311, S2CID 195069356.
Weingartner (2019). Weingartner, A. (2019), "On the constant factor in several related asymptotic estimates", Mathematics of Computation, 88 (318): 1883–1902, arXiv:1705.06349, doi:10.1090/mcom/3402, S2CID 85532616.
Weingartner (2021) Weingartner, A. (2021), "An extension of the Siegel-Walfisz theorem", Proceedings of the American Mathematical Society, 149 (11): 4699–4708, arXiv:2011.06627, doi:10.1090/proc/15607, S2CID 226956079.

jstor.org

Stewart (1954); Sierpiński (1955). Stewart, B. M. (1954), "Sums of distinct divisors", American Journal of Mathematics, 76 (4), The Johns Hopkins University Press: 779–785, doi:10.2307/2372651, JSTOR 2372651, MR 0064800. Sierpiński, Wacław (1955), "Sur une propriété des nombres naturels", Annali di Matematica Pura ed Applicata, 39 (1): 69–74, doi:10.1007/BF02410762, S2CID 121592840.

nju.edu.cn

maths.nju.edu.cn

Sun, Zhi-Wei, A Conjecture on Unit Fractions Involving Primes (PDF), archived from the original (PDF) on 2018-10-19, retrieved 2016-11-22

semanticscholar.org

api.semanticscholar.org

Stewart (1954); Sierpiński (1955). Stewart, B. M. (1954), "Sums of distinct divisors", American Journal of Mathematics, 76 (4), The Johns Hopkins University Press: 779–785, doi:10.2307/2372651, JSTOR 2372651, MR 0064800. Sierpiński, Wacław (1955), "Sur une propriété des nombres naturels", Annali di Matematica Pura ed Applicata, 39 (1): 69–74, doi:10.1007/BF02410762, S2CID 121592840.
Weingartner (2022). Weingartner, A. (2022), "Somewhat smooth numbers in short intervals", Ramanujan Journal, 60 (2): 447–453, arXiv:2105.13568, doi:10.1007/s11139-022-00552-w, S2CID 235247868.
Weingartner (2015) and Remark 1 of Pomerance & Weingartner (2021) Weingartner, A. (2015), "Practical numbers and the distribution of divisors", The Quarterly Journal of Mathematics, 66 (2): 743–758, arXiv:1405.2585, doi:10.1093/qmath/hav006. Pomerance, C.; Weingartner, A. (2021), "On primes and practical numbers", Ramanujan Journal, 57 (3): 981–1000, arXiv:2007.11062, doi:10.1007/s11139-020-00354-y, S2CID 220686445.
Weingartner (2020). Weingartner, A. (2020), "The constant factor in the asymptotic for practical numbers", International Journal of Number Theory, 16 (3): 629–638, arXiv:1906.07819, doi:10.1142/S1793042120500311, S2CID 195069356.
Weingartner (2019). Weingartner, A. (2019), "On the constant factor in several related asymptotic estimates", Mathematics of Computation, 88 (318): 1883–1902, arXiv:1705.06349, doi:10.1090/mcom/3402, S2CID 85532616.
Weingartner (2021) Weingartner, A. (2021), "An extension of the Siegel-Walfisz theorem", Proceedings of the American Mathematical Society, 149 (11): 4699–4708, arXiv:2011.06627, doi:10.1090/proc/15607, S2CID 226956079.

uwaterloo.ca

cs.uwaterloo.ca

Eppstein (2021). Eppstein, David (2021), "Egyptian fractions with denominators from sequences closed under doubling", Journal of Integer Sequences, 24: 21.8.8, arXiv:2109.12217

web.archive.org

Srinivasan (1948). Srinivasan, A. K. (1948), "Practical numbers" (PDF), Current Science, 17: 179–180, MR 0027799, archived from the original (PDF) on 2016-03-05.
Sun, Zhi-Wei, A Conjecture on Unit Fractions Involving Primes (PDF), archived from the original (PDF) on 2018-10-19, retrieved 2016-11-22