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A325469
a(n) is the number of divisors d of n such that d divides sigma(d).
4
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, ...
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Aug 16 2019
EXTENSIONS
More terms from Antti Karttunen, Aug 22 2019
STATUS
approved