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a(n) = Sum_{j=1..n} Sum_{k=1..n} sigma(j*k).
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%I #25 May 11 2024 04:25:57

%S 1,14,59,190,401,914,1499,2632,4113,6424,8645,13284,17023,23092,30715,

%T 40484,48711,63890,75351,95792,116421,139822,159911,199176,229499,

%U 267438,309283,364462,404933,482792,532553,611208,688593,772540,862471,998760,1083615,1200328

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

%C Sum_{j=1..n} sigma(j*k) ~ A069097(k) * Pi^2 * n^2 / (12*k).

%H Vaclav Kotesovec, <a href="/A372675/b372675.txt">Table of n, a(n) for n = 1..10000</a>

%H Vaclav Kotesovec, <a href="/A372675/a372675.jpg">Plot of a(n)/n^4 for n = 1..100000</a>

%F a(n) ~ c * n^4, where c = Pi^4 / (144*zeta(3)) = 0.56274...

%t Table[Sum[DivisorSigma[1, j*k], {j, 1, n}, {k, 1, n}], {n, 1, 50}]

%t s = 1; Join[{1}, Table[s += DivisorSigma[1, n^2] + 2*Sum[DivisorSigma[1, j*n], {j, 1, n - 1}], {n, 2, 50}]]

%Y Cf. A069097, A372633, A372674.

%Y Cf. A024916, A326124.

%Y Cf. A000203, A062731, A144613, A193553, A283118, A224613, A283078, A283122, A283123.

%K nonn

%O 1,2

%A _Vaclav Kotesovec_, May 10 2024