A325471 a(n) is the product of divisors d of n such that d divides sigma(d).

1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 28, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 28, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 168, 1, 1

Offset: 1

Author

Jaroslav Krizek, Aug 16 2019

Keywords

• nonn

Examples

			For n = 12, divisors d of 12: 1, 2, 3, 4, 6, 12; corresponding sigma(d): 1, 3, 4, 7, 12, 28; d divides sigma(d) for 2 divisors d: 1 and 6; a(12) = 1 * 6 = 6.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000203, A097603, A325469, A325470.

Programs

Magma

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

Mathematica

a[n_] := Times @@ Select[Divisors[n], Divisible[DivisorSigma[1, #], #] &]; Array[a, 100] (* Amiram Eldar, Aug 17 2019 *)

PARI

a(n)={vecprod([d | d<-divisors(n), sigma(d) % d==0])} \\ Andrew Howroyd, Aug 16 2019

Formula

a(A097603(n)) > 1.