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Search: id:A096442
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| A096442 |
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a(n) = Max { k>0 : denominator(S(k,2n+1)) } where S(k,s)=sum(i=1,k,i^s*H(i,2)) - H(k,2)*H(k,-s) and H(k,r)=sum(i=1,k,1/i^r) are the generalized harmonic numbers. |
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| 4, 12, 12, 20, 12, 420, 4, 60, 84, 220, 12, 1092, 4, 60, 924, 340, 12, 103740, 4, 660, 84, 92, 12, 13260, 44, 60, 1596, 580, 12, 1861860, 4, 204, 1932, 20, 132, 3838380, 4, 60, 84, 153340, 12, 1361724, 4, 1380, 77748, 940, 12, 92820, 4, 660
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The sequence D = (denominator(S(k, 2n+1)))_{k>0} is periodic for any n>0 . i.e. for n=2, D has period {1, 4, 12, 6, 6, 12, 12, 3, 1, 4, 4, 6, 6, 12, 12, 3, 3, 4, 4, 2, 6, 12, 12, 3, 3, 12, 4, 2, 2, 12, 12, 3, 3, 12, 12, 2, 2, 4, 12, 3, 3, 12, 12, 6, 2, 4, 4, 3, 3, 12, 12, 6, 6, 4, 4, 1, 3, 12, 12, 6, 6, 12, 4, 1, 1, 12, 12, 6, 6, 12, 12, 1} of length 72 and reaches 12 as maximum value, hence a(2)=12
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PROGRAM
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(PARI) H(n, r)=sum(i=1, n, 1/i^r); S(n, s)=sum(k=1, n, k^s*H(k, 2))-H(n, 2)*H(n, -s); a(n)=vecmax(vector(100, i, denominator(S(i, 2*n+1))))
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CROSSREFS
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Sequence in context: A074258 A120213 A005886 this_sequence A009115 A051434 A074138
Adjacent sequences: A096439 A096440 A096441 this_sequence A096443 A096444 A096445
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 10 2004
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