

A229861


Let sigma*_m (n) be result of applying sum of antidivisors m times to n; call n (m,k)antiperfect if sigma*_m (n) = k*n; sequence gives the (3,k)antiperfect 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
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OFFSET

1,1


COMMENTS

Tested up to n = 10^6.


LINKS

Table of n, a(n) for n=1..32.


EXAMPLE

Antidivisors of 54 are 4, 12, 36. Their sum is 52.
Again, antidivisors of 52 are 3, 5, 7, 8, 15, 21, 35. Their sum is 94.
Finally, antidivisors 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*a1)+sigma(a/2^k)*2^(k+1)6*a2; od;
if type(a/n, integer) then print(n); fi; od; end: P(10^6, 3);


CROSSREFS

Cf. A066272, A066417, A019278, A019292, A019293, A192293, A214842, A229860, A229862.
Sequence in context: A113726 A207191 A240790 * A140315 A055497 A194419
Adjacent sequences: A229858 A229859 A229860 * A229862 A229863 A229864


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



