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A247951
a(n) = Product_{i=1..n} sigma_2(i).
3
1, 5, 50, 1050, 27300, 1365000, 68250000, 5801250000, 527913750000, 68628787500000, 8372712075000000, 1758269535750000000, 298905821077500000000, 74726455269375000000000, 19428878370037500000000000, 6625247524182787500000000000
OFFSET
1,2
COMMENTS
a(n) is the product of the sum of the squared divisors of i, for i from 1 to n.
LINKS
Ramanujan's Papers, Some formulas in the analytic theory of numbers, Messenger of Mathematics, XLV, 1916, 81-84, Formula (20).
FORMULA
a(n) = Product_{i=1..n} A001157(i).
Lim_{n->infinity} (a(n) / (n!)^2)^(1/n) = A345158. - Vaclav Kotesovec, Jun 10 2021
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}]
PROG
(PARI) lista(nn) = vector(nn, n, prod(i=1, n, sigma(i, 2))) \\ Michel Marcus, Oct 01 2014
CROSSREFS
Cf. A000203 (sigma), A001157 (sigma_2), A066780 (product{i=1..n} sigma(i)), A066843, A345158, A345160.
Sequence in context: A116906 A051893 A354685 * A082100 A299353 A180976
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 01 2014
STATUS
approved