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 A324707 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). 7

%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; tsigma[n_]:= Times @@ f @@@ FactorInteger[n]; Select[Range, 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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Last modified September 30 18:15 EDT 2023. Contains 365792 sequences. (Running on oeis4.)