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.

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

Author

Paolo P. Lava, Aug 22 2014

Keywords

• nonn

Comments

Like A066860 but using anti-divisors.

Examples

			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.
		

Links

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

Crossrefs

Cf. A066272, A066860.

Programs

Maple

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);

Extensions

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