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A323757 Modified exponential perfect numbers: numbers k such that A241405(k) = 2*k. 4

%I #11 Jul 18 2019 11:39:48

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

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

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

%C 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

%H A. V. Lelechenko, <a href="https://taac.org.ua/files/a2014/proceedings/UA-2-Andrew%20Lelechenko-440.pdf">The Quest for the Generalized Perfect Numbers</a>, Theoretical and Applied Aspects of Cybernetics, Proceedings, The 4th International Scientific Conference of Students and Young Scientists, Kyiv, 2014.

%H David Moews, <a href="http://djm.cc/amicable.html">Perfect, amicable and sociable numbers</a>.

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

%t 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]

%o (PARI) f(n) = {my(f=factor(n)); prod(i=1, #f[, 1], sumdiv(f[i, 2]+1, d, f[i, 1]^(d-1)));} \\ A241405

%o isok(n) = f(n) == 2*n; \\ _Michel Marcus_, Jan 30 2019

%Y Cf. A003557, A054980, A241405.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Jan 26 2019

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)