A308652 - OEIS

%I #24 Aug 23 2019 17:12:23

%S 1,1,5,252,380562,26605273464,146392210728465000,

%T 84641321148614770425516288,7097143900835489590932722296959504144,

%U 109983275218947201453245400551817117367706036248320,397899007017966277799025689101644536884667639093655295898437500000

%N a(n) = Product_{k=1..n} sigma(n,k).

%F a(n) ~ (n!)^n.

%F a(n) ~ 2^(n/2) * Pi^(n/2) * n^(n*(2*n+1)/2) / exp(n^2-1/12).

%p with(NumberTheory): seq(product(sigma[n](k), k = 1..n), n = 0..10);

%t Table[Product[DivisorSigma[n, k], {k, 1, n}], {n, 1, 10}]

%o (PARI) a(n) = prod(k=1, n, sigma(k, n));

%o for(n=1, 10, print1(a(n), ", "))

%Y Cf. A236329, A319194.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Aug 20 2019

%E a(0)=1 prepended by _Alois P. Heinz_, Aug 23 2019