A240746 Numbers n>1 that divide the sum of their divisors and anti-divisors.

3, 19, 76, 85, 131, 139, 184, 649, 772, 1010, 1190, 3234, 3328, 3649, 3970, 4181, 5881, 11748, 13369, 29501, 65789, 286544, 830568, 2035100, 2405568, 5152800, 10515998, 13343342, 30232314, 34729314, 37548761, 44933902, 50637780, 63919409

Offset

1,1

Comments

1 and 2 have no anti-divisors.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..41

Example

The sum of the divisors of 772 is 1358 while the sum of its anti-divisors is 958. Then (1358 + 958) / 772 = 3.

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((sigma(n)+a)/n, integer) then print(n); fi; od; end: P(10^9);

Prog

(PARI) is(n)=my(k=valuation(n, 2)); (sigma(2*n+1)+sigma(2*n-1)+sigma(n>>k)<<(k+1)+sigma(n))%n==2 \\ Charles R Greathouse IV, Jun 19 2015

Crossrefs

Cf. A000203, A066417.

Sequence in context: A243142 A174286 A336589 * A027175 A093734 A099421

Adjacent sequences: A240743 A240744 A240745 * A240747 A240748 A240749

Keyword

nonn

Author

Paolo P. Lava, Apr 23 2014

Extensions

a(24)-a(34) from Michel Marcus, Jun 19 2015

Status

approved