A108640 a(n) = Product_{k=1..n} sigma_{n-k}(k), where sigma_m(k) = sum{j|k} j^m.

1, 2, 6, 60, 1260, 239904, 123263712, 872883648000, 35330106763980000, 15502816844111220549120, 32196148399600498119169883520, 2560463149313858442381787649990400000, 717635502576022020068175045395317927056000000

Offset: 1

Author

Leroy Quet, Jul 06 2005

Keywords

• nonn

Examples

			a(5) = 1^4 * (1^3 +2^3) * (1^2 +3^2) * (1^1 +2^1 +4^1) * (1^0 +5^0) = 1 * 9 * 10 * 7 * 2 = 1260.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..44

Crossrefs

Cf. A108639 (with sums).

Programs

Magma

A108639:= func< n | (&*[DivisorSigma(j, n-j): j in [0..n-1]]) >;
[A108639(n): n in [1..30]]; // G. C. Greubel, Oct 18 2023

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),i=1..n): seq(a(n),n=1..14); # Emeric Deutsch, Jul 13 2005

Mathematica

Table[Product[DivisorSigma[j,n-j], {j,0,n-1}], {n,30}] (* G. C. Greubel, Oct 18 2023 *)

PARI

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

SageMath

def A108640(n): return product(sigma(n-j,j) for j in range(n))
[A108640(n) for n in range(1,31)] # G. C. Greubel, Oct 18 2023

Extensions

More terms from Emeric Deutsch, Jul 13 2005