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A045795 Unitary-sigma 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

%I

%S 1,2,4,8,10,16,24,27,30,54,63,64,108,126,165,238,252,360,432,504,512,

%T 660,864,952,1008,1536,1728,2016,2464,2640,4032,4096,5544,10560,13824,

%U 16728,17640,23040,32256,45500,47360,60928,65536,110592,152064,153600

%N Unitary-sigma 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).

%H Donovan Johnson, <a href="/A045795/b045795.txt">Table of n, a(n) for n = 1..100</a>

%e 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.

%o (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 */

%Y Cf. A045796, A034448.

%K nonn

%O 1,2

%A _Yasutoshi Kohmoto_

%E Corrected and extended by _Jud McCranie_, Oct 28 2001

%E Missing first term added and offset corrected by _Donovan Johnson_, Mar 12 2013

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Last modified January 18 19:38 EST 2020. Contains 331029 sequences. (Running on oeis4.)