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A066860 The sum of the non-divisors of n (less than n) is a multiple of the sum of the divisors of n. 3
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 (list; graph; refs; listen; history; text; internal format)
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.

MAPLE

with(numtheory);

P:=proc(i)

local a, n;

for n from 3 to i do

  a:=(n*(n+1))/(2*sigma(n))-1; if a=trunc(a) then print(n); fi;

od;

end:

P(10000000000); # Paolo P. Lava, Dec 12 2011

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

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Last modified June 6 18:59 EDT 2020. Contains 334832 sequences. (Running on oeis4.)