A322486 - OEIS

%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