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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.
2
3, 5, 7, 8, 14, 16, 32, 41, 56, 92, 98, 114, 167, 507, 543, 946, 2524, 3433, 5186, 5566, 6596, 6707, 6874, 8104, 9615, 15690, 17386, 27024, 84026, 87667, 167786, 199282, 390982, 1023971, 1077378, 1336968, 1529394, 2054435, 2276640, 2667584, 3098834, 3978336
OFFSET
1,1
COMMENTS
Tested up to n = 10^6.
EXAMPLE
Anti-divisors of 92 are 3, 5, 8, 37, 61. Their sum is 114.
Again, anti-divisors of 114 are 4, 12, 76. Their sum is 92 and 92 / 92 = 1.
MAPLE
with(numtheory); P:=proc(q, h) local a, i, j, k, n;
for n from 3 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, 2);
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Oct 01 2013
EXTENSIONS
Offset corrected and a(34)-a(42) from Donovan Johnson, Jan 09 2014
STATUS
approved