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%I #35 Nov 15 2017 04:29:29
%S 15,20,35,95,104,119,143,207,209,287,319,323,377,464,527,559,650,779,
%T 899,923,989,1007,1023,1189,1199,1343,1349,1519,1763,1919,1952,2015,
%U 2159,2507,2759,2911,2915,2975,3239,3599,3827,4031,4199,4607,5183,5207,5249
%N 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).
%C Numbers k such that sigma(k)/(sigma(k)-k-1) is a positive integer.
%H Charles R Greathouse IV, <a href="/A294149/b294149.txt">Table of n, a(n) for n = 1..10000</a>
%F 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
%e 15 is in the sequence since sigma(15)/(sigma(15)-15-1) = 24/8 = 3.
%t Quiet@ Select[Range[2, 5300], And[IntegerQ[#], # > 1] &[#2/(#2 - #1 - 1)] & @@ {#, DivisorSigma[1, #]} &] (* _Michael De Vlieger_, Oct 24 2017 *)
%o (PARI) lista(nn) = forcomposite(n=1, nn, if (denominator(sigma(n)/(sigma(n)-n-1)) == 1, print1(n, ", "))); \\ _Michel Marcus_, Oct 24 2017
%o (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
%Y Subsequence of A002808 (composite numbers).
%Y Cf. A000203, A048050.
%Y Cf. A088831 (k=2), A063906 (k=3).
%K nonn
%O 1,1
%A _Zdenek Cervenka_, Oct 23 2017
%E Edited by _Wolfdieter Lang_, Nov 10 2017
%E Name corrected by _Michel Marcus_, Nov 12 2017
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