LINKS
G. C. Greubel, <a href="/A108640/b108640_1.txt">Table of n, a(n) for n = 1..44</a>
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G. C. Greubel, <a href="/A108640/b108640_1.txt">Table of n, a(n) for n = 1..44</a>
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a(n) = Product_{k=1 to ..n} sigma_{n-k}(k), where sigma_m(k) = sum{j|k} j^m.
G. C. Greubel, <a href="/A108640/b108640_1.txt">Table of n, a(n) for n = 1..44</a>
Table[Product[DivisorSigma[j, n-j], {j, 0, n-1}], {n, 30}] (* G. C. Greubel, Oct 18 2023 *)
(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
(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
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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
(PARI) a(n) = prod(k=1, n, sigma(k, n-k)); \\ Michel Marcus, Aug 16 2019
Cf. A108639 (with sums).
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Leroy Quet , Jul 06 2005
_Leroy Quet _ Jul 06 2005