cp's OEIS Frontend

A065080 Denominator of Sum_{k=1..n} d(k)/k, where d() = A000005().

%I A065080 #21 Aug 31 2018 09:55:13
%S A065080 1,1,3,12,60,60,420,420,420,420,4620,4620,60060,60060,60060,240240,
%T A065080 4084080,4084080,77597520,77597520,25865840,25865840,594914320,
%U A065080 1784742960,8923714800,8923714800,80313433200,80313433200,2329089562800,2329089562800,72201776446800
%N A065080 Denominator of Sum_{k=1..n} d(k)/k, where d() = A000005().
%C A065080 The old entry with this sequence number was a duplicate of A034093.
%D A065080 M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 237.
%H A065080 Harry J. Smith, <a href="/A065080/b065080.txt">Table of n, a(n) for n=1..200</a>
%H A065080 Mathematics.StackExchange, <a href="https://math.stackexchange.com/questions/471326/the-asymptotic-expansion-for-the-weighted-sum-of-divisors-sum-n-leq-x-frac">The asymptotic expansion for the weighted sum of divisors</a>, Aug 19 2013.
%F A065080 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
%e A065080 1, 2, 8/3, 41/12, 229/60, 269/60, 2003/420, 2213/420, 2353/420, 2521/420, 28571/4620, 30881/4620, ...
%p A065080 t:= 0:
%p A065080 for n from 1 to 50 do
%p A065080   t:= t + numtheory:-tau(n)/n;
%p A065080   A[n]:= denom(t);
%p A065080 od: seq(A[n], n=1..50); # _Robert Israel_, Mar 20 2018
%t A065080 Denominator[Accumulate[Table[DivisorSigma[0,n]/n,{n,40}]]] (* _Harvey P. Dale_, Jul 31 2016 *)
%o A065080 (PARI) { s=0; for (n=1, 200, s+=numdiv(n)/n; write("b065080.txt", n, " ", denominator(s)) ) } \\ _Harry J. Smith_, Oct 06 2009
%o A065080 (PARI) a(n) = denominator(sum(k=1, n, numdiv(k)/k)); \\ _Michel Marcus_, Mar 20 2018
%Y A065080 Cf. A000005, A060436.
%K A065080 nonn,frac
%O A065080 1,3
%A A065080 _N. J. A. Sloane_, Nov 02 2008