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A229862 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 (4,k)-anti-perfect numbers. 2
5, 6, 7, 8, 14, 16, 41, 46, 56, 58, 64, 92, 96, 114, 946, 3307, 3325, 5186, 5566, 6596, 6874, 7982, 8104, 14621, 17386, 27024, 44217, 45970, 84026, 91282, 135592, 167786, 1077378, 1231058, 1529394, 2667584, 2873910, 3098834, 3978336, 4292594, 4921776, 27914146 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Tested up to n = 10^6.

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

Anti-divisors of 58 are 3, 4, 5, 9, 13, 23, 39. Their sum is 96.

The only anti-divisor of 96 is 64.

Again, anti-divisors of 64 are 3, 43. Their sum is 46. Finally, anti-divisors of 46 are 3, 4, 7, 13, 31. Their sum is 58 and 58 / 58 = 1.

MAPLE

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

for n from 5 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, 4);

CROSSREFS

Cf. A066272, A066417, A019278, A019292, A019293, A192293, A214842, A229860, A229861.

Sequence in context: A047575 A014097 A219331 * A302599 A098670 A343570

Adjacent sequences:  A229859 A229860 A229861 * A229863 A229864 A229865

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Oct 01 2013

EXTENSIONS

Offset corrected and a(33)-a(42) from Donovan Johnson, Jan 09 2014

STATUS

approved

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Last modified July 26 20:56 EDT 2021. Contains 346300 sequences. (Running on oeis4.)