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A326698
a(n) is the product of divisors d of n such that sigma(d) divides n.
4
1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 36, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 36, 1, 1, 1, 4, 1, 10, 1, 1, 1, 1, 1, 36, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 36, 1, 1, 1, 1, 1, 2, 1, 784, 1, 1, 1, 180, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 36, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1
OFFSET
1,6
COMMENTS
a(A097603(n)) > 1.
See A173441 and A326697 for number and sum such divisors.
LINKS
EXAMPLE
For n = 12, divisors d of 12: 1, 2, 3, 4, 6, 12;
corresponding sigma(d): 1, 3, 4, 7, 12, 28;
sigma(d) divides n for 4 divisors d: 1, 2, 3, 6;
a(12) = 1 * 2 * 3 * 6 = 36.
MATHEMATICA
a[n_] := Times @@ Select[Divisors[n], Divisible[n, DivisorSigma[1, #] &]]; Array[a, 100] (* Amiram Eldar, Jul 21 2019 *)
PROG
(Magma) [&*[d: d in Divisors(n) | IsIntegral(n / SumOfDivisors(d))]: n in [1..100]];
(PARI) a(n) = my(p=1); fordiv(n, d, if (!(n % sigma(d)), p *= d)); p; \\ Michel Marcus, Jul 19 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jul 19 2019
STATUS
approved