

A045795


Unitarysigma sigma multiply perfect numbers n such that usigma(sigma(n)) = m*n for some integer m, where if sigma(n) = product p(i)^r(i) then usigma(sigma(n)) = product (p(i)^r(i)+1).


3



1, 2, 4, 8, 10, 16, 24, 27, 30, 54, 63, 64, 108, 126, 165, 238, 252, 360, 432, 504, 512, 660, 864, 952, 1008, 1536, 1728, 2016, 2464, 2640, 4032, 4096, 5544, 10560, 13824, 16728, 17640, 23040, 32256, 45500, 47360, 60928, 65536, 110592, 152064, 153600
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OFFSET

1,2


LINKS

Donovan Johnson, Table of n, a(n) for n = 1..100


EXAMPLE

For example, sigma(10) = 18 = 2*3^2. Usigma(18) = (2+1)*(9+1) = 30, divisible by 10, so 10 is in the sequence. Sigma(24) = 60 = 2^2*3*5, usigma(60) = 5*4*6 = 120, divisible by 24, so 24 is in the sequence.


PROG

(PARI) for(n=1, 10^9, s=sigma(n); om=omega(s); f=factorint(s); pr=1; for(j=1, om, pr=pr*(f[j, 1]^f[j, 2]+1)); if(pr%n==0, print(n))) /* Donovan Johnson, Mar 12 2013 */


CROSSREFS

Cf. A045796, A034448.
Sequence in context: A102248 A161374 A272062 * A226816 A291165 A083655
Adjacent sequences: A045792 A045793 A045794 * A045796 A045797 A045798


KEYWORD

nonn


AUTHOR

Yasutoshi Kohmoto


EXTENSIONS

Corrected and extended by Jud McCranie, Oct 28 2001
Missing first term added and offset corrected by Donovan Johnson, Mar 12 2013


STATUS

approved



