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A065080 Denominator of Sum_{k=1..n} d(k)/k, where d() = A000005(). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The old entry with this sequence number was a duplicate of A034093.

REFERENCES

M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 237.

LINKS

Harry J. Smith, Table of n, a(n) for n=1..200

Mathematics.StackExchange, The asymptotic expansion for the weighted sum of divisors, Aug 19 2013.

FORMULA

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

EXAMPLE

1, 2, 8/3, 41/12, 229/60, 269/60, 2003/420, 2213/420, 2353/420, 2521/420, 28571/4620, 30881/4620, ...

MAPLE

t:= 0:

for n from 1 to 50 do

  t:= t + numtheory:-tau(n)/n;

  A[n]:= denom(t);

od: seq(A[n], n=1..50); # Robert Israel, Mar 20 2018

MATHEMATICA

Denominator[Accumulate[Table[DivisorSigma[0, n]/n, {n, 40}]]] (* Harvey P. Dale, Jul 31 2016 *)

PROG

(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

CROSSREFS

Cf. A000005, A060436.

Sequence in context: A020102 A277179 A201013 * A114419 A090830 A233283

Adjacent sequences:  A065077 A065078 A065079 * A065081 A065082 A065083

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Nov 02 2008

STATUS

approved

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Last modified September 29 10:06 EDT 2020. Contains 337428 sequences. (Running on oeis4.)