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
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
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
Comments