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
Keywords
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) = 2.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..16384
- Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Programs
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Magma
[#[d: d in Divisors(n) | IsIntegral(SumOfDivisors(d) / d)] : n in [1..100]];
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Mathematica
a[n_] := DivisorSum[n, 1 &, Divisible[DivisorSigma[1, #], #] &]; Array[a, 100] (* Amiram Eldar, Aug 17 2019 *)
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PARI
a(n)={sumdiv(n, d, sigma(d) % d == 0)} \\ Andrew Howroyd, Aug 16 2019
Formula
a(A097603(n)) > 1.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A335830. - Amiram Eldar, Apr 16 2025
Extensions
More terms from Antti Karttunen, Aug 22 2019
Comments