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

1,2

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

Links

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000203, A024816, A066860.

Sequence in context: A031022 A194542 A076646 * A091791 A281660 A244324

Adjacent sequences: A076614 A076615 A076616 * A076618 A076619 A076620

Keyword

nonn

Author

Joseph L. Pe, Oct 22 2002

Extensions

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

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

Status

approved