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

1,6

Links

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

Formula

a(A097603(n)) > 1.

Example

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.

Mathematica

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

Prog

(Magma) [&*[d: d in Divisors(n) | IsIntegral(SumOfDivisors(d) / d)] : n in [1..100]]
(PARI) a(n)={vecprod([d | d<-divisors(n), sigma(d) % d==0])} \\ Andrew Howroyd, Aug 16 2019

Crossrefs

Cf. A000203, A097603, A325469, A325470.

Sequence in context: A202917 A324396 A234959 * A167155 A369465 A268731

Adjacent sequences: A325468 A325469 A325470 * A325472 A325473 A325474

Keyword

nonn

Author

Jaroslav Krizek, Aug 16 2019

Status

approved