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Search: id:A097504
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| A097504 |
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Denominator 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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2
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| 1, 2, 6, 6, 60, 20, 140, 70, 280, 2520, 27720, 6930, 360360, 360360, 360360, 30030, 12252240, 1361360, 77597520, 29099070, 25865840, 11085360, 118982864, 446185740, 267711444, 1274816400, 2974571600, 10039179150, 2329089562800
(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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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(denom(b[n]), n=1..32); (Deutsch)
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CROSSREFS
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Cf. A096663.
Sequence in context: A069260 A056603 A019198 this_sequence A130726 A011044 A131212
Adjacent sequences: A097501 A097502 A097503 this_sequence A097505 A097506 A097507
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), 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 (maxal(AT)cs.ucsd.edu), Apr 13 2005
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