A066860 The sum of the non-divisors of n (less than n) is a multiple of the sum of the divisors of n.

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

Offset: 1

Author

Joseph L. Pe, Jan 25 2002

Keywords

• nonn

Examples

			Divisors of 15 = {1, 3, 5, 15}, which sum to 24. Non-divisors of 15 less than 15 = {2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14}, which sum to 96, a multiple of 24. So 15 is a term of the sequence.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A000203, A024816, A076617, A232324.

Programs

Mathematica

f[n_] := Module[{a, b, c}, a = Divisors[n]; b = Apply[Plus, Complement[Range[1, n], a]]; c = Apply[Plus, a]; Mod[b, c] == 0]; Do[If[f[n] == True, Print[n]], {n, 3, 23519}]
Select[Range[3, 10000], Mod[# (# + 1)/2, DivisorSigma[1, #]] == 0 &] (* T. D. Noe, Nov 27 2013 *)

Formula

a(n) = A076617(n+2). - Alex Ratushnyak, Jul 02 2013

A232324(a(n)) = A024816(a(n)) mod A000203(a(n)) = 0. - Jaroslav Krizek, Nov 25 2013

Extensions

More terms from Lior Manor, Feb 10 2002