cp's OEIS Frontend

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.

%I A229860 #9 Jan 09 2014 03:53:48
%S A229860 3,5,7,8,14,16,32,41,56,92,98,114,167,507,543,946,2524,3433,5186,5566,
%T A229860 6596,6707,6874,8104,9615,15690,17386,27024,84026,87667,167786,199282,
%U A229860 390982,1023971,1077378,1336968,1529394,2054435,2276640,2667584,3098834,3978336
%N 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.
%C A229860 Tested up to n = 10^6.
%e A229860 Anti-divisors of 92 are 3, 5, 8, 37, 61. Their sum is 114.
%e A229860 Again, anti-divisors of 114 are 4, 12, 76. Their sum is 92 and 92 / 92 = 1.
%p A229860 with(numtheory); P:=proc(q,h) local a,i,j,k,n;
%p A229860 for n from 3 to q do a:=n; for i from 1 to h do
%p A229860 k:=0; j:=a; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
%p A229860 a:=sigma(2*a+1)+sigma(2*a-1)+sigma(a/2^k)*2^(k+1)-6*a-2; od;
%p A229860 if type(a/n,integer) then print(n); fi; od; end: P(10^6,2);
%Y A229860 Cf. A066272, A066417, A019278, A019292, A019293, A192293, A214842, A229861, A229862.
%K A229860 nonn
%O A229860 1,1
%A A229860 _Paolo P. Lava_, Oct 01 2013
%E A229860 Offset corrected and a(34)-a(42) from _Donovan Johnson_, Jan 09 2014