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

1, 2, 15, 20, 24, 95, 104, 207, 224, 287, 464, 1023, 1199, 1952, 4095, 4607, 8036, 12095, 15872, 16895, 19359, 22932, 23519, 28799, 45440, 45695, 54144, 77375, 101567, 102024, 130304, 159599, 163295, 223199, 296207, 317184, 352799, 522752, 524160, 635904

Offset: 1

Author

Joseph L. Pe, Oct 22 2002

Keywords

• nonn

Comments

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.

Numbers k such that A232324(k) = antisigma(k) mod sigma(k) = A024816(n) mod A000203(n) = 0. - Jaroslav Krizek, Jan 24 2014

Examples

			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.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000203, A024816, A066860.

Programs

Mathematica

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
Select[Range[640000],Divisible[(#(#+1))/2,DivisorSigma[1,#]]&] (* Harvey P. Dale, Aug 01 2019 *)

PARI

is(n)=n*(n+1)/2%sigma(n)==0 \\ Charles R Greathouse IV, May 02 2013

Formula

a(n+2) = A066860(n) - Alex Ratushnyak, Jul 02 2013

Extensions

New name from J. M. Bergot, May 02 2013

More terms from T. D. Noe, May 02 2013