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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 (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 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);

CROSSREFS

Cf. A066272, A066417, A019278, A019292, A019293, A192293, A214842, A229861, A229862.

Sequence in context: A032420 A127458 A039003 * A081453 A345343 A200655

Adjacent sequences:  A229857 A229858 A229859 * A229861 A229862 A229863

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

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Last modified August 5 00:15 EDT 2021. Contains 346456 sequences. (Running on oeis4.)