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).

6, 60, 90, 36720, 47520, 8173440, 22276800, 126463680, 597542400, 4201148160, 287704872000, 1632485836800

Offset: 1

Author

Amiram Eldar, Mar 11 2019

Keywords

• nonn
• more

Comments

Also in the sequence is 21623407345626345971712000.

a(13) > 5*10^12. - Giovanni Resta, Mar 14 2019

Examples

			36720 is in the sequence since its sum of tri-unitary divisors is A324706(36720) = 73440 = 2 * 36720.
		

Crossrefs

Cf. A000396, A002827, A007357, A322486, A324706, A324708, A324709.

Programs

Mathematica

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# &]

Extensions

a(11)-a(12) from Giovanni Resta, Mar 14 2019