A294149 Numbers k such that the sum of divisors of k is divisible by the sum of nontrivial divisors of k (that is, excluding 1 and k).

15, 20, 35, 95, 104, 119, 143, 207, 209, 287, 319, 323, 377, 464, 527, 559, 650, 779, 899, 923, 989, 1007, 1023, 1189, 1199, 1343, 1349, 1519, 1763, 1919, 1952, 2015, 2159, 2507, 2759, 2911, 2915, 2975, 3239, 3599, 3827, 4031, 4199, 4607, 5183, 5207, 5249

Offset

1,1

Comments

Numbers k such that sigma(k)/(sigma(k)-k-1) is a positive integer.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

This sequence gives all numbers a(n) in increasing order which satisfy A000203(a(n))/A048050(a(n)) = A000203(a(n))/(A000203(a(n)) - (a(n)+1)) = k(n), with a positive integer k(n) for n >= 1. - Wolfdieter Lang, Nov 10 2017

Example

15 is in the sequence since sigma(15)/(sigma(15)-15-1) = 24/8 = 3.

Mathematica

Quiet@ Select[Range[2, 5300], And[IntegerQ[#], # > 1] &[#2/(#2 - #1 - 1)] & @@ {#, DivisorSigma[1, #]} &] (* Michael De Vlieger, Oct 24 2017 *)

Prog

(PARI) lista(nn) = forcomposite(n=1, nn, if (denominator(sigma(n)/(sigma(n)-n-1)) == 1, print1(n, ", "))); \\ Michel Marcus, Oct 24 2017
(PARI) list(lim)=my(v=List(), s, t); forfactored(n=9, lim\1, s=sigma(n); t=s-n[1]-1; if(t && s%t==0, listput(v, n[1]))); Vec(v) \\ Charles R Greathouse IV, Nov 11 2017

Crossrefs

Subsequence of A002808 (composite numbers).

Cf. A000203, A048050.

Cf. A088831 (k=2), A063906 (k=3).

Sequence in context: A111200 A088494 A109659 * A065148 A093028 A105506

Adjacent sequences: A294146 A294147 A294148 * A294150 A294151 A294152

Keyword

nonn

Author

Zdenek Cervenka, Oct 23 2017

Extensions

Edited by Wolfdieter Lang, Nov 10 2017

Name corrected by Michel Marcus, Nov 12 2017

Status

approved