A229860 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 (2,k)-anti-perfect numbers.

3, 5, 7, 8, 14, 16, 32, 41, 56, 92, 98, 114, 167, 507, 543, 946, 2524, 3433, 5186, 5566, 6596, 6707, 6874, 8104, 9615, 15690, 17386, 27024, 84026, 87667, 167786, 199282, 390982, 1023971, 1077378, 1336968, 1529394, 2054435, 2276640, 2667584, 3098834, 3978336

Offset: 1

Author

Paolo P. Lava, Oct 01 2013

Keywords

• nonn

Comments

Tested up to n = 10^6.

Examples

			Anti-divisors of 92 are 3, 5, 8, 37, 61. Their sum is 114.
Again, anti-divisors of 114 are 4, 12, 76. Their sum is 92 and 92 / 92 = 1.
		

Crossrefs

Cf. A066272, A066417, A019278, A019292, A019293, A192293, A214842, A229861, A229862.

Programs

Maple

with(numtheory); P:=proc(q,h) local a,i,j,k,n;
for n from 3 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(10^6,2);

Extensions

Offset corrected and a(34)-a(42) from Donovan Johnson, Jan 09 2014