A308652 a(n) = Product_{k=1..n} sigma(n,k).

1, 1, 5, 252, 380562, 26605273464, 146392210728465000, 84641321148614770425516288, 7097143900835489590932722296959504144, 109983275218947201453245400551817117367706036248320, 397899007017966277799025689101644536884667639093655295898437500000

Offset: 0

Author

Vaclav Kotesovec, Aug 20 2019

Keywords

• nonn

Crossrefs

Cf. A236329, A319194.

Programs

Maple

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

Mathematica

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

PARI

a(n) = prod(k=1, n, sigma(k, n));
for(n=1, 10, print1(a(n), ", "))

Formula

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

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

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 23 2019