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

1,1

Comments

Tested up to n = 10^6.

Links

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

Example

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.

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);

Crossrefs

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

Sequence in context: A032420 A127458 A039003 * A081453 A352105 A345343

Adjacent sequences: A229857 A229858 A229859 * A229861 A229862 A229863

Keyword

nonn

Author

Paolo P. Lava, Oct 01 2013

Extensions

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

Status

approved