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

1,6

Comments

a(A097603(n)) > 1.

See A173441 and A326697 for number and sum such divisors.

Links

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

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

Cf. A000203, A000961, A173441, A326697.

Sequence in context: A327156 A114171 A154243 * A299432 A252911 A176820

Adjacent sequences: A326695 A326696 A326697 * A326699 A326700 A326701

Keyword

nonn

Author

Jaroslav Krizek, Jul 19 2019

Status

approved