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

Author

Paolo P. Lava, Oct 01 2013

Keywords

• nonn

Comments

Tested up to n = 10^6.

Examples

			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.
		

Crossrefs

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

Programs

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);

Extensions

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