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A372675 a(n) = Sum_{j=1..n} Sum_{k=1..n} sigma(j*k).

%I A372675 #25 May 11 2024 04:25:57
%S A372675 1,14,59,190,401,914,1499,2632,4113,6424,8645,13284,17023,23092,30715,
%T A372675 40484,48711,63890,75351,95792,116421,139822,159911,199176,229499,
%U A372675 267438,309283,364462,404933,482792,532553,611208,688593,772540,862471,998760,1083615,1200328
%N A372675 a(n) = Sum_{j=1..n} Sum_{k=1..n} sigma(j*k).
%C A372675 Sum_{j=1..n} sigma(j*k) ~ A069097(k) * Pi^2 * n^2 / (12*k).
%H A372675 Vaclav Kotesovec, <a href="/A372675/b372675.txt">Table of n, a(n) for n = 1..10000</a>
%H A372675 Vaclav Kotesovec, <a href="/A372675/a372675.jpg">Plot of a(n)/n^4 for n = 1..100000</a>
%F A372675 a(n) ~ c * n^4, where c = Pi^4 / (144*zeta(3)) = 0.56274...
%t A372675 Table[Sum[DivisorSigma[1, j*k], {j, 1, n}, {k, 1, n}], {n, 1, 50}]
%t A372675 s = 1; Join[{1}, Table[s += DivisorSigma[1, n^2] + 2*Sum[DivisorSigma[1, j*n], {j, 1, n - 1}], {n, 2, 50}]]
%Y A372675 Cf. A069097, A372633, A372674.
%Y A372675 Cf. A024916, A326124.
%Y A372675 Cf. A000203, A062731, A144613, A193553, A283118, A224613, A283078, A283122, A283123.
%K A372675 nonn
%O A372675 1,2
%A A372675 _Vaclav Kotesovec_, May 10 2024