

A090997


Numbers m such that the numerator of the Bernoulli number B(m) is divisible by a square.


7



50, 98, 150, 196, 228, 242, 250, 284, 338, 350, 392, 450, 484, 490, 550, 578, 650, 676, 686, 722, 726, 750, 784, 850, 914, 950, 968, 980, 1014, 1050, 1058, 1078, 1150, 1156, 1184, 1250, 1274, 1350, 1352, 1372, 1434, 1444, 1450, 1452, 1550, 1568, 1616
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

It appears that all terms that are divisible by p^2 and do not belong to A090943 are of the form 2*k*p^2, where p is a prime and k > 0 is an integer. Also, all numbers in A090943 are terms because they are divisible by the squares of irregular primes in A094095. The corresponding smallest primes p such that their squares divide terms are listed in A090987.  Alexander Adamchuk, Aug 19 2006
A subsequence of the current sequence is A122270, which are the numbers m such that the numerator of the Bernoulli number B(m) is divisible by a cube. Another subsequence of the current sequence is A122272, which are the numbers m such that the numerator of the Bernoulli number B(m) is divisible by p^4, where p is a prime. Note that the numerator of the Bernoulli number B(6250) is divisible by 5^5.  Alexander Adamchuk, Aug 28 2006


LINKS

Alexander Adamchuk, Aug 28 2006, Table of n, a(n) for n = 1..152 (term 3886 added by Daniel Suteu)
The Bernoulli Number Page, Table of factors of the numerators of Bernoulli numbers Bn in the range n = 2..10000, 2018.
S. S. Wagstaff, Jr, Prime factors of the absolute values of Bernoulli numerators, 2018.


EXAMPLE

a(3) = 150 because numerator(B(150)) == 0 (mod 5^2).


CROSSREFS

Cf. A000367, A090943, A094095. For the smallest square factor, see A090987.
Cf. A122270, A122271, A122272, A122273.
Sequence in context: A335480 A255585 A260901 * A141757 A248023 A328253
Adjacent sequences: A090994 A090995 A090996 * A090998 A090999 A091000


KEYWORD

nonn


AUTHOR

Hans Havermann, Feb 28 2004


EXTENSIONS

In view of the phrase "it appears", it is not clear to me that the correctness of this sequence has been rigorously established.  N. J. A. Sloane, Aug 26 2006
More terms from Alexander Adamchuk, Aug 19 2006
More terms from Alexander Adamchuk, Aug 28 2006
Various sections edited by Petros Hadjicostas, May 12 2020
Incorrect term 294 removed by Daniel Suteu, May 21 2020


STATUS

approved



