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%I #10 Jul 17 2021 07:26:23
%S 6,60,90,36720,47520,8173440,22276800,126463680,597542400,4201148160,
%T 287704872000,1632485836800
%N Tri-unitary perfect numbers: numbers k such that tsigma(k) = 2k, where tsigma(k) is the sum of the tri-unitary divisors of k (A324706).
%C Also in the sequence is 21623407345626345971712000.
%C a(13) > 5*10^12. - _Giovanni Resta_, Mar 14 2019
%e 36720 is in the sequence since its sum of tri-unitary divisors is A324706(36720) = 73440 = 2 * 36720.
%t f[p_, e_] := If[e == 3, (p^4-1)/(p-1), If[e==6, (p^8-1)/(p^2-1), p^e+1]]; tsigma[1]=1; tsigma[n_]:= Times @@ f @@@ FactorInteger[n]; Select[Range[50000], tsigma[#]==2# &]
%Y Cf. A000396, A002827, A007357, A322486, A324706, A324708, A324709.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Mar 11 2019
%E a(11)-a(12) from _Giovanni Resta_, Mar 14 2019
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