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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).
1
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. A088831 (k=2), A063906 (k=3).
Sequence in context: A111200 A088494 A109659 * A065148 A093028 A105506
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