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Search: id:A096663
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| A096663 |
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Numerator of b(n), where sum{k=1 to oo} b(k)/k^r = 1/(sum{k=1 to oo} H(k)/k^r). H(k) = sum{j=1 to k} 1/j, the k_th harmonic number. |
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+0
2
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| 1, -3, -11, 1, -137, 61, -363, 11, 149, 9881, -83711, -3391, -1145993, 1631353, 1821257, 3397, -42142223, -1565387, -275295799, -20644219, 151619971, 59515289, -444316699, -203021927, 374167685, 7248582529, 950047851, -8741096671, -9227046511387, -22795769741183
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For r = integer >= 2, sum{k=1 to oo} b(k)/k^r also equals 1/(zeta(r+1)(r/2 +1) -(1/2)sum{j=2 to r-1} zeta(j)zeta(r+1-j)), where zeta(n) is sum{k=1 to oo} 1/k^n.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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b(1)=1; for n>=2, b(n) = -sum{k|n, k>=2} H(k) b(n/k)
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EXAMPLE
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1,-3/2,-11/6,1/6,-137/60,61/20,-363/140,...
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MAPLE
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with(numtheory): H:=n->sum(1/j, j=1..n): b[1]:=1: for n from 2 to 32 do div:=sort(convert(divisors(n), list)):b[n]:=-sum(H(div[i])*b[n/div[i]], i=2..nops(div)) od: seq(numer(b[n]), n=1..32); (Deutsch)
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CROSSREFS
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Cf. A097504.
Sequence in context: A092528 A069604 A098332 this_sequence A133369 A110123 A110221
Adjacent sequences: A096660 A096661 A096662 this_sequence A096664 A096665 A096666
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KEYWORD
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frac,sign
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AUTHOR
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Leroy Quet Aug 25 2004
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Max Alekseyev (maxale(AT)gmail.com), Apr 13 2005
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