A356043 a(n) = Sum_{k=1..n} sigma_3(k) * floor(n/k).
1, 11, 40, 123, 250, 540, 885, 1553, 2339, 3609, 4942, 7349, 9548, 12998, 16681, 22030, 26945, 34805, 41666, 52207, 62212, 75542, 87711, 107083, 122961, 144951, 166177, 194812, 219203, 256033, 285826, 328624, 367281, 416431, 460246, 525484, 576139, 644749, 708520
Offset: 1
Keywords
Programs
-
Mathematica
Table[Sum[DivisorSigma[3, k]*Floor[n/k], {k, 1, n}], {n, 1, 50}] (* Vaclav Kotesovec, Aug 07 2022 *) -
PARI
a(n) = sum(k=1, n, sigma(k, 3)*(n\k));
-
PARI
a(n) = sum(k=1, n, sumdiv(k, d, d^3*numdiv(k/d)));
-
PARI
my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k, 3)*x^k/(1-x^k))/(1-x))
Formula
a(n) = Sum_{k=1..n} Sum_{d|k} d^3 * tau(k/d).
G.f.: (1/(1-x)) * Sum_{k>=1} sigma_3(k) * x^k/(1 - x^k).
a(n) ~ Pi^8 * n^4 / 32400. - Vaclav Kotesovec, Aug 07 2022