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

1,1

Links

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

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

Example

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.

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 *)

Crossrefs

Cf. A000203, A024816, A076617, A232324.

Sequence in context: A014603 A070222 A143321 * A120159 A163602 A074236

Adjacent sequences: A066857 A066858 A066859 * A066861 A066862 A066863

Keyword

nonn

Author

Joseph L. Pe, Jan 25 2002

Extensions

More terms from Lior Manor Feb 10 2002

Status

approved