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%I #20 Aug 26 2022 07:29:16
%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: numbers k such that A061765(k) = m*k for some integer m.
%H Donovan Johnson, <a href="/A045795/b045795.txt">Table of n, a(n) for n = 1..100</a>
%e Sigma(10) = 18 = 2*3^2, usigma(18) = (2+1)*(9+1) = 30, divisible by 10, so 10 is in the sequence.
%e Sigma(24) = 60 = 2^2*3*5, usigma(60) = 5*4*6 = 120, divisible by 24, so 24 is in the sequence.
%t q[n_] := Divisible[Times @@ (1 + Power @@@ FactorInteger[DivisorSigma[1, n]]), n]; Select[Range[200000], q] (* _Amiram Eldar_, Aug 26 2022 *)
%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. A000203, A034448, A045796, A061765.
%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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