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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.
2
4, 5, 8, 32, 41, 54, 56, 68, 123, 946, 1494, 1856, 2056, 5186, 6874, 8104, 10419, 17386, 27024, 31100, 84026, 167786, 272089, 733253, 812600, 1188000, 1544579, 2667584, 4921776, 16360708, 21524990, 27914146
OFFSET
1,1
COMMENTS
Tested up to n = 10^6.
EXAMPLE
Anti-divisors of 54 are 4, 12, 36. Their sum is 52.
Again, anti-divisors of 52 are 3, 5, 7, 8, 15, 21, 35. Their sum is 94.
Finally, anti-divisors of 94 are 3, 4, 7, 9, 11, 17, 21, 27, 63. Their sum is 162 and 162 / 54 = 3.
MAPLE
with(numtheory); P:=proc(q, h) local a, i, j, k, n;
for n from 4 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, 3);
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Oct 01 2013
EXTENSIONS
Offset corrected and a(26)-a(32) from Donovan Johnson, Jan 09 2014
STATUS
approved