cp's OEIS Frontend

A090997 Numbers m such that the numerator of the Bernoulli number B(m) is divisible by a square.

%I A090997 #33 May 21 2020 03:57:19
%S A090997 50,98,150,196,228,242,250,284,338,350,392,450,484,490,550,578,650,
%T A090997 676,686,722,726,750,784,850,914,950,968,980,1014,1050,1058,1078,1150,
%U A090997 1156,1184,1250,1274,1350,1352,1372,1434,1444,1450,1452,1550,1568,1616
%N A090997 Numbers m such that the numerator of the Bernoulli number B(m) is divisible by a square.
%C A090997 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
%C A090997 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
%H A090997 Alexander Adamchuk, Aug 28 2006, <a href="/A090997/b090997.txt">Table of n, a(n) for n = 1..152</a> (term 3886 added by Daniel Suteu)
%H A090997 The Bernoulli Number Page, <a href="https://www.bernoulli.org/download/bn_factors.txt">Table of factors of the numerators of Bernoulli numbers Bn in the range n = 2..10000</a>, 2018.
%H A090997 S. S. Wagstaff, Jr, <a href="http://www.cerias.purdue.edu/homes/ssw/bernoulli/bnum">Prime factors of the absolute values of Bernoulli numerators</a>, 2018.
%e A090997 a(3) = 150 because numerator(B(150)) == 0 (mod 5^2).
%Y A090997 Cf. A000367, A090943, A094095. For the smallest square factor, see A090987.
%Y A090997 Cf. A122270, A122271, A122272, A122273.
%K A090997 nonn
%O A090997 1,1
%A A090997 _Hans Havermann_, Feb 28 2004
%E A090997 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
%E A090997 More terms from _Alexander Adamchuk_, Aug 19 2006
%E A090997 More terms from _Alexander Adamchuk_, Aug 28 2006
%E A090997 Various sections edited by _Petros Hadjicostas_, May 12 2020
%E A090997 Incorrect term 294 removed by _Daniel Suteu_, May 21 2020