A325469 - OEIS

%I #16 Sep 08 2022 08:46:24

%S 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,

%T 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,

%U 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

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

%C 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, ...

%H Antti Karttunen, <a href="/A325469/b325469.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A325469/a325469.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(A097603(n)) > 1.

%e 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.

%t a[n_] := DivisorSum[n, 1 &, Divisible[DivisorSigma[1, #], #] &];  Array[a, 100] (* _Amiram Eldar_, Aug 17 2019 *)

%o (Magma) [#[d: d in Divisors(n) | IsIntegral(SumOfDivisors(d) / d)] : n in [1..100]]

%o (PARI) a(n)={sumdiv(n, d, sigma(d) % d == 0)} \\ _Andrew Howroyd_, Aug 16 2019

%Y Cf. A000203, A097603, A325470, A325471.

%K nonn

%O 1,6

%A _Jaroslav Krizek_, Aug 16 2019

%E More terms from _Antti Karttunen_, Aug 22 2019