login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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.
2

%I #10 Jan 09 2014 03:53:59

%S 4,5,8,32,41,54,56,68,123,946,1494,1856,2056,5186,6874,8104,10419,

%T 17386,27024,31100,84026,167786,272089,733253,812600,1188000,1544579,

%U 2667584,4921776,16360708,21524990,27914146

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

%C Tested up to n = 10^6.

%e Anti-divisors of 54 are 4, 12, 36. Their sum is 52.

%e Again, anti-divisors of 52 are 3, 5, 7, 8, 15, 21, 35. Their sum is 94.

%e Finally, anti-divisors of 94 are 3, 4, 7, 9, 11, 17, 21, 27, 63. Their sum is 162 and 162 / 54 = 3.

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

%p for n from 4 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(10^6,3);

%Y Cf. A066272, A066417, A019278, A019292, A019293, A192293, A214842, A229860, A229862.

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, Oct 01 2013

%E Offset corrected and a(26)-a(32) from _Donovan Johnson_, Jan 09 2014