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A090997
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Numbers m such that the numerator of the Bernoulli number B(m) is divisible by a square.
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7
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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)
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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a(3) = 150 because numerator(B(150)) == 0 (mod 5^2).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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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
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STATUS
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approved
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