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

1,1

Comments

Like A066860 but using anti-divisors.

Links

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

Example

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.

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);

Crossrefs

Cf. A066272, A066860.

Sequence in context: A241097 A267725 A161762 * A291035 A005913 A056690

Adjacent sequences: A245646 A245647 A245648 * A245650 A245651 A245652

Keyword

nonn

Author

Paolo P. Lava, Aug 22 2014

Extensions

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

Status

approved