A374974 a(n) = Sum_{k=1..n-1} sigma(k) * sigma_2(n-k).
0, 1, 8, 29, 78, 170, 324, 579, 918, 1472, 2106, 3126, 4174, 5904, 7500, 10189, 12458, 16563, 19574, 25312, 29538, 37320, 42456, 53472, 59456, 73482, 81806, 99268, 108352, 132084, 141814, 170411, 184076, 217438, 231322, 276579, 289408, 340624, 361128, 419734
Offset: 1
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Table[Sum[DivisorSigma[1, k]*DivisorSigma[2, n-k], {k, 1, n-1}], {n, 1, 50}] (* Vaclav Kotesovec, Sep 19 2024 *) -
PARI
a(n) = sum(k=1, n-1, sigma(k, 1)*sigma(n-k, 2));
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PARI
my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, k*x^k/(1-x^k))*sum(k=1, N, k^2*x^k/(1-x^k))))
Formula
G.f.: ( Sum_{k>=1} k * x^k/(1 - x^k) ) * ( Sum_{k>=1} k^2 * x^k/(1 - x^k) ).
Sum_{k=1..n} a(k) ~ Pi^2 * zeta(3) * n^5 / 360. - Vaclav Kotesovec, Sep 19 2024
Comments