login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (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..32.

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);

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 19 10:33 EDT 2019. Contains 322252 sequences. (Running on oeis4.)