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A323757 Modified exponential perfect numbers: numbers k such that A241405(k) = 2*k. 2
6, 60, 90, 264, 3960, 8736, 87360, 131040, 1868160 (list; graph; refs; listen; history; text; internal format)
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).

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: A189000 A007358 A322486 * A324707 A007357 A002827

Adjacent sequences:  A323754 A323755 A323756 * A323758 A323759 A323760

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Jan 26 2019

STATUS

approved

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Last modified June 20 00:47 EDT 2019. Contains 324223 sequences. (Running on oeis4.)