%I #16 Jul 23 2024 10:48:55
%S 0,0,8,42,72,240,240,630,728,1296,1080,3080,1848,3744,4368,6510,4320,
%T 10608,6120,14364,12160,15120,11088,30360,17112,25200,26000,39312,
%U 22680,58464,27840,58590,47616,57024,53856,108290,47880,79920,78736,133380,65520,157440
%N a(n) = (n - 1) * (n - 2) * sigma(n).
%H William Craig, Jan-Willem van Ittersum, and Ken Ono, <a href="https://arxiv.org/abs/2405.06451">Integer partitions detect the primes</a>, arXiv:2405.06451v2 [math.CO], Jul 10 2024.
%F a(n) = A002378(n-2) * A000203(n).
%F a(n) >= 8 * A002127(n) and the equal sign only holds if n is 1 or prime.
%t a[n_]:= (n - 1) * (n - 2) * DivisorSigma[1,n]; Array[a,42] (* _Stefano Spezia_, Jul 23 2024 *)
%o (PARI) a(n) = (n-1)*(n-2)*sigma(n);
%Y Cf. A000203, A002127, A002378, A060043, A078837.
%K nonn
%O 1,3
%A _Seiichi Manyama_, Jul 23 2024