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A065080
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Denominator of Sum_{k=1..n} d(k)/k, where d() = A000005().
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2
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1, 1, 3, 12, 60, 60, 420, 420, 420, 420, 4620, 4620, 60060, 60060, 60060, 240240, 4084080, 4084080, 77597520, 77597520, 25865840, 25865840, 594914320, 1784742960, 8923714800, 8923714800, 80313433200, 80313433200, 2329089562800, 2329089562800, 72201776446800
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OFFSET
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1,3
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COMMENTS
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The old entry with this sequence number was a duplicate of A034093.
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REFERENCES
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M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 237.
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LINKS
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FORMULA
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Sum_{k=1..n} A000005(k)/k = A060436(n)/a(n) ~ log(n)^2/2 + 2*gamma*log(n) + gamma^2 - 2*gamma_1, where gamma is the Euler-Mascheroni constant A001620 and gamma_1 is the first Stieltjes constant A082633. - Vaclav Kotesovec, Aug 30 2018
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EXAMPLE
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1, 2, 8/3, 41/12, 229/60, 269/60, 2003/420, 2213/420, 2353/420, 2521/420, 28571/4620, 30881/4620, ...
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MAPLE
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t:= 0:
for n from 1 to 50 do
t:= t + numtheory:-tau(n)/n;
A[n]:= denom(t);
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MATHEMATICA
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Denominator[Accumulate[Table[DivisorSigma[0, n]/n, {n, 40}]]] (* Harvey P. Dale, Jul 31 2016 *)
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PROG
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(PARI) { s=0; for (n=1, 200, s+=numdiv(n)/n; write("b065080.txt", n, " ", denominator(s)) ) } \\ Harry J. Smith, Oct 06 2009
(PARI) a(n) = denominator(sum(k=1, n, numdiv(k)/k)); \\ Michel Marcus, Mar 20 2018
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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