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a(n) = Sum_{i+j+k+l=n, i,j,k,l >= 1} sigma(i)*sigma(j)*sigma(k)*sigma(l).
4

%I #22 Sep 20 2024 05:33:51

%S 0,0,0,1,12,70,280,885,2364,5586,12000,23870,44660,79272,134768,

%T 220565,349440,538270,807840,1187004,1706840,2415150,3354120,4601870,

%U 6209612,8303610,10935960,14309640,18460260,23708184,30044000,37967925,47368480,59022432,72633816

%N a(n) = Sum_{i+j+k+l=n, i,j,k,l >= 1} sigma(i)*sigma(j)*sigma(k)*sigma(l).

%H Vaclav Kotesovec, <a href="/A374977/b374977.txt">Table of n, a(n) for n = 1..10000</a>

%F 4-fold convolution of A000203.

%F Convolution of A000203 and A374951.

%F Convolution of A000385 with itself.

%F a(n) = Sum_{i=1..n-1} A000203(i)*A374951(n-i).

%F a(n) = Sum_{i=1..n-3} A000385(i)*A000385(n-i-2).

%F Column k=4 of A319083.

%F Sum_{k=1..n} a(k) ~ Pi^8 * n^8 / 52254720. - _Vaclav Kotesovec_, Sep 20 2024

%o (Python)

%o from sympy import divisor_sigma

%o def A374977(n): return sum((5*divisor_sigma(i+1,3)-(5+6*i)*divisor_sigma(i+1))*(5*divisor_sigma(n-i-1,3)-(5+6*(n-i-2))*divisor_sigma(n-i-1)) for i in range(1,n-2))//144

%Y Cf. A000203, A000385, A319083, A374951.

%K nonn

%O 1,5

%A _Chai Wah Wu_, Jul 26 2024