A229861 Let sigma*_m (n) be result of applying sum of anti-divisors m times to n; call n (m,k)-anti-perfect if sigma*_m (n) = k*n; sequence gives the (3,k)-anti-perfect numbers.

4, 5, 8, 32, 41, 54, 56, 68, 123, 946, 1494, 1856, 2056, 5186, 6874, 8104, 10419, 17386, 27024, 31100, 84026, 167786, 272089, 733253, 812600, 1188000, 1544579, 2667584, 4921776, 16360708, 21524990, 27914146

Offset

1,1

Comments

Tested up to n = 10^6.

Links

Table of n, a(n) for n=1..32.

Example

Anti-divisors of 54 are 4, 12, 36. Their sum is 52.
Again, anti-divisors of 52 are 3, 5, 7, 8, 15, 21, 35. Their sum is 94.
Finally, anti-divisors of 94 are 3, 4, 7, 9, 11, 17, 21, 27, 63. Their sum is 162 and 162 / 54 = 3.

Maple

with(numtheory); P:=proc(q, h) local a, i, j, k, n;
for n from 4 to q do a:=n; for i from 1 to h do
k:=0; j:=a; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
a:=sigma(2*a+1)+sigma(2*a-1)+sigma(a/2^k)*2^(k+1)-6*a-2; od;
if type(a/n, integer) then print(n); fi; od; end: P(10^6, 3);

Crossrefs

Cf. A066272, A066417, A019278, A019292, A019293, A192293, A214842, A229860, A229862.

Sequence in context: A113726 A207191 A240790 * A140315 A055497 A194419

Adjacent sequences: A229858 A229859 A229860 * A229862 A229863 A229864

Keyword

nonn,more

Author

Paolo P. Lava, Oct 01 2013

Extensions

Offset corrected and a(26)-a(32) from Donovan Johnson, Jan 09 2014

Status

approved