A066860 -id:A066860 - cp's OEIS frontend

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

Joseph L. Pe, Oct 22 2002

nonn

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

			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.

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

Cf. A000203, A024816, A066860.

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 *)

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

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

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

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

A245649 Numbers n such that the sum of the non-anti-divisors of n is a multiple of the sum of the anti-divisors of n.

Original entry on oeis.org

3, 5, 12, 27, 39, 41, 48, 63, 324, 1275, 1599, 2259, 2304, 3124, 3724, 14295, 19464, 21659, 40655, 44659, 262983, 338064, 485463, 505407, 686700, 696795, 898528, 1595384, 10377100, 12332927, 14452991, 14883967, 21024479, 23068975, 25527535, 30971420, 37471143

Offset: 1

Paolo P. Lava, Aug 22 2014

nonn

Like A066860 but using anti-divisors.

			The anti-divisors of 14295 are 2, 6, 10, 11, 23, 30, 113, 253, 1243, 1906, 2599, 5718, 9530 which sum is 21444. The sum of the non-anti-divisors is 14295*14296 / 2 - 21444 = 102159216 and 102159216 / 21444 = 4764.

Lars Blomberg, Table of n, a(n) for n = 1..70

Cf. A066272, A066860.

with(numtheory):P:=proc(q) local a,j,k,n;
for n from 3 to q do
k:=0; j:=n; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
if type(n*(n+1)/(2*a),integer) then print(n); fi;
od; end: P(10^10);

a(28)-a(37) from Lars Blomberg, Oct 27 2014

cp's OEIS Frontend

A076617 Numbers k such that sum of the divisors d of k divides 1 + 2 + ... + k = k(k+1)/2.

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