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%I #13 Sep 09 2018 05:03:53
%S 1,7,16,40,55,109,130,210,264,354,387,603,642,768,903,1143,1194,1518,
%T 1575,1935,2124,2322,2391,3111,3261,3495,3765,4269,4356,5166,5259,
%U 5931,6228,6534,6849,8145,8256,8598,8949,10149,10272,11406,11535,12327,13137,13551
%N a(n) = Sum_{k=1..n} k * tau_3(k), where tau_3 is A007425.
%H Vaclav Kotesovec, <a href="/A318750/b318750.txt">Table of n, a(n) for n = 1..100000</a>
%H Vaclav Kotesovec, <a href="/A318750/a318750_1.jpg">Graph - The asymptotic ratio (1000000 terms)</a>
%F a(n) = Sum_{k=1..n} A034718(k).
%F a(n) ~ n^2 * (log(n)^2 + (6*g-1)*log(n) + 6*g^2 - 3*g - 6*g1 + 1/2) / 4, where g is the Euler-Mascheroni constant A001620 and g1 is the first Stieltjes constant A082633. - _Vaclav Kotesovec_, Sep 09 2018
%t Accumulate[Table[n*Sum[DivisorSigma[0, d], {d, Divisors[n]}], {n, 1, 100}]]
%t (* Asymptotics: *) n^2 * (Log[n]^2 + (6*EulerGamma - 1)*Log[n] + 6*EulerGamma^2 - 3*EulerGamma - 6*StieltjesGamma[1] + 1/2) / 4 (* _Vaclav Kotesovec_, Sep 09 2018 *)
%Y Cf. A007425, A034718, A061201, A318413, A318414.
%K nonn
%O 1,2
%A _Vaclav Kotesovec_, Sep 02 2018
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