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 A328132 Exponential (2,3)-perfect numbers: numbers m such that esigma(esigma(m)) = 3m, where esigma(m) is the sum of exponential divisors of m (A051377). 1
 300, 2100, 3300, 3900, 5100, 5700, 6900, 8700, 9300, 11100, 12100, 12300, 12900, 14100, 15900, 17700, 18300, 20100, 21300, 21900, 23100, 23700, 23760, 24900, 26700, 27300, 29100, 30300, 30900, 32100, 32700, 33900, 35700, 38100, 39300, 39900, 41100, 41700, 42900 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The exponential version of A019281. REFERENCES J. Hanumanthachari, V. V. Subrahmanya Sastri, and V. Srinivasan, On e-perfect numbers, Math. Student, Vol. 46, No. 1 (1978), pp. 71-80. József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 1, p. 53. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA 300 is in the sequence since esigma(300) = 540, and esigma(540) = 900 = 3*300. MATHEMATICA f[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ f @@@ FactorInteger[n]; espQ[n_] := esigma[esigma[n]] == 3n; Select[Range[50000], espQ] CROSSREFS Cf. A019281, A051377, A064012. Sequence in context: A237773 A188252 A128391 * A234412 A234406 A092715 Adjacent sequences: A328129 A328130 A328131 * A328133 A328134 A328135 KEYWORD nonn AUTHOR Amiram Eldar, Oct 04 2019 STATUS approved

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Last modified September 30 21:59 EDT 2023. Contains 365812 sequences. (Running on oeis4.)