A283970 Integers m such that m divides sigma_2(m) - k where k is some divisor of m.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 15, 17, 19, 23, 25, 29, 30, 31, 35, 36, 37, 40, 41, 43, 47, 48, 49, 50, 53, 59, 60, 61, 65, 67, 71, 73, 76, 79, 83, 89, 97, 101, 103, 107, 109, 113, 120, 121, 127, 130, 131, 132, 136, 137, 139, 140, 149, 150, 151, 157, 163, 167, 169, 173, 175, 179, 180

Offset

1,2

Links

Table of n, a(n) for n=1..69.

Example

2 is in this sequence because 2 divides A001157(2) - 1 = 5 - 1 = 4.

Mathematica

Select[Range@ 180, Function[n, Total@ Boole@ Map[Divisible[ DivisorSigma[2, n] - #, n] &, Divisors@ n] > 0]] (* Michael De Vlieger, Mar 19 2017 *)

Prog

(Magma) [[n: k in [1..n] | Denominator(n/k) eq 1 and
Denominator(((DivisorSigma(2, n))-k)/n) eq 1]: n in [1..100]];
(PARI) isok(n) = fordiv(n, d, if (!((sigma(n, 2) - d) % n), return (1))); \\ Michel Marcus, Mar 18 2017

Crossrefs

Supersequence of A166684.

Cf. A001157 (sigma_2(n): sum of squares of divisors of n), A205523 (integers n such that n divides sigma_1(n) - i where i is some divisor of n), A284082.

Sequence in context: A348782 A331119 A366169 * A376268 A121166 A249017

Adjacent sequences: A283967 A283968 A283969 * A283971 A283972 A283973

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 18 2017

Status

approved