A229862 - OEIS

%I #9 Jan 09 2014 03:54:10

%S 5,6,7,8,14,16,41,46,56,58,64,92,96,114,946,3307,3325,5186,5566,6596,

%T 6874,7982,8104,14621,17386,27024,44217,45970,84026,91282,135592,

%U 167786,1077378,1231058,1529394,2667584,2873910,3098834,3978336,4292594,4921776,27914146

%N 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.

%C Tested up to n = 10^6.

%e Anti-divisors of 58 are 3, 4, 5, 9, 13, 23, 39. Their sum is 96.

%e The only anti-divisor of 96 is 64.

%e 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.

%p with(numtheory); P:=proc(q,h) local a,i,j,k,n;

%p for n from 5 to q do a:=n; for i from 1 to h do

%p k:=0; j:=a; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;

%p a:=sigma(2*a+1)+sigma(2*a-1)+sigma(a/2^k)*2^(k+1)-6*a-2; od;

%p if type(a/n,integer) then print(n); fi; od; end: P(10^6,4);

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

%K nonn

%O 1,1

%A _Paolo P. Lava_, Oct 01 2013

%E Offset corrected and a(33)-a(42) from _Donovan Johnson_, Jan 09 2014