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%I #13 Jul 17 2021 06:59:46
%S 6,60,90,264,3960,4560,8736,13770,131040,384384,605880,5765760,
%T 20049120,882161280,23253135360
%N Semi-unitary perfect numbers: numbers k such that susigma(k) = 2k, where susigma(k) is the sum of the semi-unitary divisors of k (A322485).
%C a(16) <= 1846273228800. - _David A. Corneth_, Dec 11 2018
%e 264 is in the sequence since its sum of semi-unitary divisors is susigma(264) = 528 = 2 * 264.
%t f[p_, e_] := (p^Floor[(e+1)/2] - 1)/(p-1) + p^e; susigma[n_] := If[n==1, 1, Times @@ (f @@@ FactorInteger[n])]; aQ[n_] := susigma[n]==2n; Select[Range[10000], aQ]
%o (PARI) ssu(n) = {my(f = factor(n)); for (k=1, #f~, my(p=f[k,1], e=f[k,2]); f[k,1] = (p^((e+1)\2) - 1)/(p-1) + p^e; f[k,2] = 1;); factorback(f);} \\ A322485
%o isok(n) = ssu(n) == 2*n; \\ _Michel Marcus_, Dec 14 2018
%Y Cf. A000396, A002827, A322485.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Dec 11 2018
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