A323757 Modified exponential perfect numbers: numbers k such that A241405(k) = 2*k.

6, 60, 90, 264, 3960, 8736, 87360, 131040, 1868160

Offset: 1

Author

Amiram Eldar, Jan 26 2019

Keywords

• nonn
• more

Comments

Each term of this sequence corresponds to a primitive e-perfect number (A054980, see formula and Andrew Lelechenko's comment in A241405).

Also in the sequence are 1028004440830371164160, 20546724596095746048000, and 146361946186458562560000 (corresponding to the 3 additional terms of A054980 given by Andrew Lelechenko). - Amiram Eldar, Jul 18 2019

Links

• A. V. Lelechenko, The Quest for the Generalized Perfect Numbers, Theoretical and Applied Aspects of Cybernetics, Proceedings, The 4th International Scientific Conference of Students and Young Scientists, Kyiv, 2014.
• David Moews, Perfect, amicable and sociable numbers.

Crossrefs

Cf. A003557, A054980, A241405.

Programs

Mathematica

f[p_, e_] := DivisorSum[e+1, p^(#-1)&]; mesigma[1]=1; mesigma[n_] := Times @@ f @@@FactorInteger@n; mePerfectQ[n_] := mesigma[n]==2n; Select[Range[10000], mePerfectQ]

PARI

f(n) = {my(f=factor(n)); prod(i=1, #f[, 1], sumdiv(f[i, 2]+1, d, f[i, 1]^(d-1)));} \\ A241405
isok(n) = f(n) == 2*n; \\ Michel Marcus, Jan 30 2019

Formula

a(n) = A003557(A054980(n)).