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A067656
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Numbers n such that n!*B(2n) is an integer, where B(2n) are the Bernoulli numbers.
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3
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7, 13, 17, 19, 24, 25, 27, 31, 32, 34, 37, 38, 43, 45, 47, 49, 55, 57, 59, 61, 62, 64, 67, 71, 73, 76, 77, 79, 80, 84, 85, 87, 91, 92, 93, 94, 97, 101, 103, 104, 107, 109, 110, 115, 117, 118, 121, 122, 123, 124, 127, 129, 132, 133, 137, 139, 142, 143, 144, 145, 147
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A045979(n), Bernoulli numbers with denominators 6, are included in the sequence.
Also numbers n such that both n+1 and 2n+1 are not prime. - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 05 2006
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LINKS
| Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 05 2006, Table of n, a(n) for n = 1..565
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FORMULA
| Also numbers n>1 such that A000330[n] = Sum[k^2,{k,1,n}] = n(n+1)(2n+1)/6 divides A001044[n] = Product[k^2,{k,1,n}] = (n!)^2. Also numbers n>1 such that Numerator[n(n+1)(2n+1)/6 /(n!)^2] = 1. - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 05 2006
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MATHEMATICA
| Select[Range[2, 1000], Numerator[ #(#+1)(2#+1)/6/#!^2]==1&] - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 05 2006
Select[Range[1000], !PrimeQ[ #+1]&&!PrimeQ[2#+1]&] - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 05 2006
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CROSSREFS
| Cf. A000330, A001044.
Cf. A166602. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 14 2010]
Sequence in context: A144426 A118942 * A166602 A079697 A079695 A079698
Adjacent sequences: A067653 A067654 A067655 * A067657 A067658 A067659
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2002
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