A325469 a(n) is the number of divisors d of n such that d divides sigma(d).

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1

Offset

1,6

Comments

Sequence of the smallest numbers m with n divisors d such that d divides sigma(d) for n >= 1: 1, 6, 84, 672, 3360, 30240, 393120, ...

Links

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

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

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) = 2.

Mathematica

a[n_] := DivisorSum[n, 1 &, 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)={sumdiv(n, d, sigma(d) % d == 0)} \\ Andrew Howroyd, Aug 16 2019

Crossrefs

Cf. A000203, A097603, A325470, A325471.

Sequence in context: A319689 A303824 A106751 * A278567 A043279 A050433

Adjacent sequences: A325466 A325467 A325468 * A325470 A325471 A325472

Keyword

nonn

Author

Jaroslav Krizek, Aug 16 2019

Extensions

More terms from Antti Karttunen, Aug 22 2019

Status

approved