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

1, 14, 59, 190, 401, 914, 1499, 2632, 4113, 6424, 8645, 13284, 17023, 23092, 30715, 40484, 48711, 63890, 75351, 95792, 116421, 139822, 159911, 199176, 229499, 267438, 309283, 364462, 404933, 482792, 532553, 611208, 688593, 772540, 862471, 998760, 1083615, 1200328

Offset: 1

Author

Vaclav Kotesovec, May 10 2024

Keywords

• nonn

Comments

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

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
• Vaclav Kotesovec, Plot of a(n)/n^4 for n = 1..100000

Crossrefs

Cf. A069097, A372633, A372674.

Cf. A024916, A326124.

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

Programs

Mathematica

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

Formula

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