A326698 a(n) is the product of divisors d of n such that sigma(d) divides n.

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

Author

Jaroslav Krizek, Jul 19 2019

Keywords

• nonn

Comments

a(A097603(n)) > 1.

See A173441 and A326697 for number and sum such divisors.

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000203, A000961, A173441, A326697.

Programs

Magma

[&*[d: d in Divisors(n) | IsIntegral(n / SumOfDivisors(d))]: n in [1..100]];

Mathematica

a[n_] := Times @@ Select[Divisors[n], Divisible[n, DivisorSigma[1, #] &]]; Array[a, 100] (* Amiram Eldar, Jul 21 2019 *)

PARI

a(n) = my(p=1); fordiv(n, d, if (!(n % sigma(d)), p *= d)); p; \\ Michel Marcus, Jul 19 2019