A325470 a(n) is the sum of divisors d of n such that d divides sigma(d).

1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 29, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 29, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 35, 1, 1

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

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 = 7.

Mathematica

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

Crossrefs

Cf. A000203, A097603, A325469, A325471.

Sequence in context: A101027 A129408 A339748 * A240831 A170824 A248909

Adjacent sequences: A325467 A325468 A325469 * A325471 A325472 A325473

Keyword

nonn

Author

Jaroslav Krizek, Aug 16 2019

Status

approved