A345160 a(n) = Product_{k=1..n} sigma_3(k).

1, 9, 252, 18396, 2317896, 584109792, 200933768448, 117546254542080, 88982514688354560, 100906171656594071040, 134407020646583302625280, 274727950201616270566072320, 603852034543152562704226959360, 1869525898945600334132286666178560

Offset: 1

Author

Vaclav Kotesovec, Jun 10 2021

Keywords

• nonn

Comments

Partial products of A001158.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..180
• Ramanujan's Papers, Some formulas in the analytic theory of numbers, Messenger of Mathematics, XLV, 1916, 81-84, Formula (20).

Crossrefs

Cf. A001158, A066843, A066780, A247951, A345159.

Programs

Mathematica

Table[Product[DivisorSigma[3, k], {k, 1, n}], {n, 1, 20}]
FoldList[Times,DivisorSigma[3,Range[20]]] (* Harvey P. Dale, Sep 18 2023 *)

PARI

a(n) = prod(k=1, n, sigma(k, 3)); \\ Michel Marcus, Jun 10 2021

Formula

Lim_{n->infinity} (a(n) / (n!)^3)^(1/n) = A345159.