A229862 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 (4,k)-anti-perfect numbers.

5, 6, 7, 8, 14, 16, 41, 46, 56, 58, 64, 92, 96, 114, 946, 3307, 3325, 5186, 5566, 6596, 6874, 7982, 8104, 14621, 17386, 27024, 44217, 45970, 84026, 91282, 135592, 167786, 1077378, 1231058, 1529394, 2667584, 2873910, 3098834, 3978336, 4292594, 4921776, 27914146

Offset

1,1

Comments

Tested up to n = 10^6.

Links

Table of n, a(n) for n=1..42.

Example

Anti-divisors of 58 are 3, 4, 5, 9, 13, 23, 39. Their sum is 96.
The only anti-divisor of 96 is 64.
Again, anti-divisors of 64 are 3, 43. Their sum is 46. Finally, anti-divisors of 46 are 3, 4, 7, 13, 31. Their sum is 58 and 58 / 58 = 1.

Maple

with(numtheory); P:=proc(q, h) local a, i, j, k, n;
for n from 5 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, 4);

Crossrefs

Cf. A066272, A066417, A019278, A019292, A019293, A192293, A214842, A229860, A229861.

Sequence in context: A047575 A014097 A219331 * A302599 A098670 A343570

Adjacent sequences: A229859 A229860 A229861 * A229863 A229864 A229865

Keyword

nonn

Author

Paolo P. Lava, Oct 01 2013

Extensions

Offset corrected and a(33)-a(42) from Donovan Johnson, Jan 09 2014

Status

approved