

A108640


a(n) = Product_{k=1..n} sigma_{nk}(k), where sigma_m(k) = sum{jk} j^m.


1



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

1,2


LINKS



EXAMPLE

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.


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


MATHEMATICA

Table[Product[DivisorSigma[j, nj], {j, 0, n1}], {n, 30}] (* G. C. Greubel, Oct 18 2023 *)


PROG

(PARI) a(n) = prod(k=1, n, sigma(k, nk)); \\ Michel Marcus, Aug 16 2019
(Magma)
A108639:= func< n  (&*[DivisorSigma(j, nj): j in [0..n1]]) >;
(SageMath)
def A108640(n): return product(sigma(nj, j) for j in range(n))


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



