STATUS
proposed
approved
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Revision History for A090943
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Even numbers n such that N(n) is divisible by a nontrivial square, say m^2 with gcd(n,m) = 1, where N(n) is the numerator of the Bernoulli number B(n). The smallest numbers m are given in A094095.
(history; published version)
(history; published version)
STATUS
editing
proposed
LINKS
Charles Weibel, <a href="https://dx.doi.org/10.1007/978-3-540-27855-9_5">Algebraic K-Theory of Rings of Integers in Local and Global Fields</a>, in: E. Friedlander and D. Grayson (eds), Handbook of K-Theory, Springer, Berlin, Heidelberg, Vol 1, 2005, pp. 139-190; see Example 96 on p. 180.
Charles Weibel, <a href="https://dx.doi.org/10.1007/978-3-540-27855-9_5">Algebraic K-Theory of Rings of Integers in Local and Global Fields</a>, in: E. Friedlander and D. Grayson (eds), Handbook of K-Theory, Springer, Berlin, Heidelberg, Vol 1, 2005, pp. 139-190; see Example 96 on p. 180.
STATUS
proposed
editing
STATUS
editing
proposed
NAME
Even numbers n such that N(n) is divisible by a nontrivial square, say m^2 with gcd(n,m) = 1, where N(n) is the numerator of the Bernoulli number B(n). The smallest numbers m are given in A094095.
EXTENSIONS
Addition of the word "smallest" in the name by Petros Hadjicostas, May 12 2020
LINKS
C. Charles Weibel, <a href="https://dx.doi.org/10.1007/978-3-540-27855-9_5">Algebraic K-Theory of Rings of Integers in Local and Global Fields</a>, in: E. Friedlander and D. Grayson (eds), Handbook of K-Theory, Springer, Berlin, Heidelberg, Vol 1, 2005, pp. 139-190; see Example 96 on p. 180.
LINKS
C. Weibel, <a href="https://dx.doi.org/10.1007/978-3-540-27855-9_5">Algebraic K-Theory of Rings of Integers in Local and Global Fields</a>, Example 96 on page 180 of in: E. Friedlander Eand D., Grayson D. (eds) , Handbook of K-Theory (2005). , Springer, Berlin, Heidelberg, Vol 1, 2005, pp. 139-190; see Example 96 on p. 180.
NAME
Even numbers n such that N(n) is divisible by a nontrivial square, m^2, say and m^2 with gcd(n,m) = 1, where N(n) is the numerator of the Bernoulli number B(n). The numbers m are given in A094095.
COMMENTS
This sequence consists of the union of an infinite number of arithmetic progressions. Let p be an irregular prime and let {m1, m2, ...} be even numbers < p*(p-1) such that p^2 | N(mi). Then each pair (p, mi) is a second-order irregular pair. This leads to the arithmetic progression n = mi + p*(p-1)*k for each i and for k = 0, 1, 2, 3, ... If we restrict the sequence to those pairs with mi < 10000, we find that only the pairs (37, 284), (59, 914), (67, 3292), (101, 5768), (103, 228), (157, 6302) and (271, 1434) contribute terms to this sequence.
LINKS
C. Weibel, <a href="https://dx.doi.org/10.1007/978-3-540-27855-9_5">Algebraic K-Theory of Rings of Integers in Local and Global Fields</a>, Example 96 on page 180 of Friedlander E., Grayson D. (eds) Handbook of K-Theory (2005). Springer, Berlin, Heidelberg, Vol 1.
S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/bernoulli/full.pdf">Prime divisors of the Bernoulli and Euler numbers</a>, 2018.
STATUS
approved
editing
STATUS
editing
approved