cp's OEIS Frontend

A229861 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 (3,k)-anti-perfect numbers.

%I A229861 #10 Jan 09 2014 03:53:59
%S A229861 4,5,8,32,41,54,56,68,123,946,1494,1856,2056,5186,6874,8104,10419,
%T A229861 17386,27024,31100,84026,167786,272089,733253,812600,1188000,1544579,
%U A229861 2667584,4921776,16360708,21524990,27914146
%N A229861 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 (3,k)-anti-perfect numbers.
%C A229861 Tested up to n = 10^6.
%e A229861 Anti-divisors of 54 are 4, 12, 36. Their sum is 52.
%e A229861 Again, anti-divisors of 52 are 3, 5, 7, 8, 15, 21, 35. Their sum is 94.
%e A229861 Finally, anti-divisors of 94 are 3, 4, 7, 9, 11, 17, 21, 27, 63. Their sum is 162 and 162 / 54 = 3.
%p A229861 with(numtheory); P:=proc(q,h) local a,i,j,k,n;
%p A229861 for n from 4 to q do a:=n; for i from 1 to h do
%p A229861 k:=0; j:=a; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
%p A229861 a:=sigma(2*a+1)+sigma(2*a-1)+sigma(a/2^k)*2^(k+1)-6*a-2; od;
%p A229861 if type(a/n,integer) then print(n); fi; od; end: P(10^6,3);
%Y A229861 Cf. A066272, A066417, A019278, A019292, A019293, A192293, A214842, A229860, A229862.
%K A229861 nonn,more
%O A229861 1,1
%A A229861 _Paolo P. Lava_, Oct 01 2013
%E A229861 Offset corrected and a(26)-a(32) from _Donovan Johnson_, Jan 09 2014