A108699 a(n) = Product{k=1 to n} sigma_{n-k+1}(k), where sigma_m(k) = sum{j|k} j^m.

1, 3, 20, 630, 59976, 61631856, 218220912000, 11776702254660000, 3875704211027805137280, 16098074199800249059584941760, 426743858218976407063631274998400000

Offset

1,2

Links

Table of n, a(n) for n=1..11.

Example

a(5) = 1^5 * (1^4 +2^4) * (1^3 +3^3) * (1^2 +2^2 +4^2) * (1^1 +5^1) = 1 * 17 * 28 * 21 * 6 = 59976.

Maple

with(numtheory): s:=proc(n, k) local div: div:=divisors(n): sum(div[j]^k, j=1..tau(n)) end: a:=n->product(s(i, n-i+1), i=1..n): seq(a(n), n=1..13); # Emeric Deutsch, Jul 13 2005

Prog

(PARI) a(n) = prod(k=1, n, sigma(k, n-k+1)); \\ Michel Marcus, Aug 16 2019

Crossrefs

Cf. A108672 (with sum).

Sequence in context: A174972 A300917 A089943 * A162134 A296408 A002857

Adjacent sequences: A108696 A108697 A108698 * A108700 A108701 A108702

Keyword

nonn

Author

Leroy Quet, Jul 07 2005

Extensions

More terms from Emeric Deutsch, Jul 13 2005

Status

approved