cp's OEIS Frontend

A076617 Numbers k such that sum of the divisors d of k divides 1 + 2 + ... + k = k(k+1)/2.

%I A076617 #35 Feb 21 2024 10:53:27
%S A076617 1,2,15,20,24,95,104,207,224,287,464,1023,1199,1952,4095,4607,8036,
%T A076617 12095,15872,16895,19359,22932,23519,28799,45440,45695,54144,77375,
%U A076617 101567,102024,130304,159599,163295,223199,296207,317184,352799,522752,524160,635904
%N A076617 Numbers k such that sum of the divisors d of k divides 1 + 2 + ... + k = k(k+1)/2.
%C A076617 Alternately, numbers k such that sum of the divisors d of k divides the sum of the non-divisors d' of k, where 1 <= d, d' <= k.
%C A076617 Numbers k such that A232324(k) = antisigma(k) mod sigma(k) = A024816(n) mod A000203(n) = 0. - _Jaroslav Krizek_, Jan 24 2014
%H A076617 Donovan Johnson, <a href="/A076617/b076617.txt">Table of n, a(n) for n = 1..200</a>
%F A076617 a(n+2) = A066860(n) - _Alex Ratushnyak_, Jul 02 2013
%e A076617 The sum of the divisors of 15 is sigma(15) = 24; the sum of the non-divisors of 15 that are between 1 and 15 is 2 + 4 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 = 96. Since 24 divides 96, 15 is a term of the sequence.
%t A076617 a = {}; Do[ s = DivisorSigma[1, i]; n = (i (i + 1) / 2) - s; If[Mod[n, s] == 0, a = Append[a, i]], {i, 1, 10^5}]; a
%t A076617 Select[Range[640000],Divisible[(#(#+1))/2,DivisorSigma[1,#]]&] (* _Harvey P. Dale_, Aug 01 2019 *)
%o A076617 (PARI) is(n)=n*(n+1)/2%sigma(n)==0 \\ _Charles R Greathouse IV_, May 02 2013
%Y A076617 Cf. A000203, A024816, A066860.
%K A076617 nonn
%O A076617 1,2
%A A076617 _Joseph L. Pe_, Oct 22 2002
%E A076617 New name from _J. M. Bergot_, May 02 2013
%E A076617 More terms from _T. D. Noe_, May 02 2013