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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

%I

%S 15,20,24,95,104,207,224,287,464,1023,1199,1952,4095,4607,8036,12095,

%T 15872,16895,19359,22932,23519,28799,45440,45695,54144,77375,101567,

%U 102024,130304,159599,163295,223199,296207,317184,352799,522752,524160

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

%H Donovan Johnson, <a href="/A066860/b066860.txt">Table of n, a(n) for n = 1..300</a>

%F a(n) = A076617(n+2) - _Alex Ratushnyak_, Jul 02 2013.

%F A232324(a(n)) = A024816(a(n)) mod A000203(a(n)) = 0. -_Jaroslav Krizek_, Nov 25 2013

%e 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.

%p with(numtheory);

%p P:=proc(i)

%p local a,n;

%p for n from 3 to i do

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

%p od;

%p end:

%p P(10000000000); # _Paolo P. Lava_, Dec 12 2011

%t 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}]

%t Select[Range[3, 10000], Mod[# (# + 1)/2, DivisorSigma[1, #]] == 0 &] (* _T. D. Noe_, Nov 27 2013 *)

%Y Cf. A000203, A024816, A076617, A232324.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Jan 25 2002

%E More terms from _Lior Manor_ Feb 10 2002

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Last modified July 5 04:30 EDT 2020. Contains 335459 sequences. (Running on oeis4.)