A247951 a(n) = Product_{i=1..n} sigma_2(i).

1, 5, 50, 1050, 27300, 1365000, 68250000, 5801250000, 527913750000, 68628787500000, 8372712075000000, 1758269535750000000, 298905821077500000000, 74726455269375000000000, 19428878370037500000000000, 6625247524182787500000000000

Offset: 1

Author

Wesley Ivan Hurt, Oct 01 2014

Keywords

• nonn
• easy

Comments

a(n) is the product of the sum of the squared divisors of i, for i from 1 to n.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..248
• Vaclav Kotesovec, Plot of (a(n)/(n!)^2)^(1/n) for n = 1..100000
• Ramanujan's Papers, Some formulas in the analytic theory of numbers, Messenger of Mathematics, XLV, 1916, 81-84, Formula (20).

Crossrefs

Cf. A000203 (sigma), A001157 (sigma_2), A066780 (product{i=1..n} sigma(i)), A066843, A345158, A345160.

Programs

Maple

with(numtheory): A247951:=n->mul(sigma[2](i),i=1..n): seq(A247951(n), n=1..20);

Mathematica

Table[Product[DivisorSigma[2, i], {i, n}], {n, 20}]

PARI

lista(nn) = vector(nn, n, prod(i=1, n, sigma(i, 2))) \\ Michel Marcus, Oct 01 2014

Formula

a(n) = Product_{i=1..n} A001157(i).

Lim_{n->infinity} (a(n) / (n!)^2)^(1/n) = A345158. - Vaclav Kotesovec, Jun 10 2021