21 (number) (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "21 (number)" in English language version.

refsWebsite

Global rank English rank

742^nd place

538^th place

274^th place

309^th place

2^nd place

2^nd place

5^th place

5^th place

1,923^rd place

1,068^th place

doi.org

Cohen, Henri (2007). "Consequences of the Hasse–Minkowski Theorem". Number Theory Volume I: Tools and Diophantine Equations. Graduate Texts in Mathematics. Vol. 239 (1st ed.). Springer. pp. 312–314. doi:10.1007/978-0-387-49923-9. ISBN 978-0-387-49922-2. OCLC 493636622. Zbl 1119.11001.

oeis.org

On the other hand, the largest member of an integer quadratic matrix representative of all numbers is 15, $\Phi _{s}(\mathbb {Z} _{\geq 0})=\{1,2,3,5,6,7,10,14,\mathbf {15} \}$ where the aliquot sum of 33 is 15, the second such number to have this sum after 16 (A001065); see also, 15 and 290 theorems. In this sequence, the sum of all members is $63=3\times 21.$
Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A001748". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
"Sloane's A016105 : Blum integers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
"Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
"Sloane's A000567 : Octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
"Sloane's A001006 : Motzkin numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
"Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
"Sloane's A005349 : Niven (or Harshad) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
"Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
Sloane, N. J. A. (ed.). "Sequence A005847 (Imaginary quadratic fields with class number 2 (a finite sequence).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-19.
Sloane, N. J. A. (ed.). "Sequence A000203 (The sum of the divisors of n. Also called sigma_1(n).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-19.
Sloane, N. J. A. (ed.). "Sequence A000396 (Perfect numbers k: k is equal to the sum of the proper divisors of k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-19.
Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers: a(n) binomial(n+1,2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-19.
Sloane, N. J. A. (ed.). "Sequence A028442 (Numbers k such that Mertens's function M(k) (A002321) is zero.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-19.
Sloane, N. J. A. (ed.). "Sequence A154363 (Numbers from Bhargava's prime-universality criterion theorem)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-10-13.
Sloane, N. J. A. (ed.). "Sequence A116582 (Numbers from Bhargava's 33 theorem.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-10-09.

springer.com

link.springer.com

Cohen, Henri (2007). "Consequences of the Hasse–Minkowski Theorem". Number Theory Volume I: Tools and Diophantine Equations. Graduate Texts in Mathematics. Vol. 239 (1st ed.). Springer. pp. 312–314. doi:10.1007/978-0-387-49923-9. ISBN 978-0-387-49922-2. OCLC 493636622. Zbl 1119.11001.

worldcat.org

search.worldcat.org

Cohen, Henri (2007). "Consequences of the Hasse–Minkowski Theorem". Number Theory Volume I: Tools and Diophantine Equations. Graduate Texts in Mathematics. Vol. 239 (1st ed.). Springer. pp. 312–314. doi:10.1007/978-0-387-49923-9. ISBN 978-0-387-49922-2. OCLC 493636622. Zbl 1119.11001.

zbmath.org

Cohen, Henri (2007). "Consequences of the Hasse–Minkowski Theorem". Number Theory Volume I: Tools and Diophantine Equations. Graduate Texts in Mathematics. Vol. 239 (1st ed.). Springer. pp. 312–314. doi:10.1007/978-0-387-49923-9. ISBN 978-0-387-49922-2. OCLC 493636622. Zbl 1119.11001.