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

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

Offset

1,1

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

Table of n, a(n) for n=1..9.

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.

Formula

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

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]

Prog

(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

Crossrefs

Cf. A003557, A054980, A241405.

Sequence in context: A007358 A334406 A322486 * A331108 A324707 A007357

Adjacent sequences: A323754 A323755 A323756 * A323758 A323759 A323760

Keyword

nonn,more

Author

Amiram Eldar, Jan 26 2019

Status

approved