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
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