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A307822
The number of e-perfect numbers below 10^n.
2
0, 1, 8, 87, 871, 8690, 86940, 869417, 8694205, 86941922
OFFSET
1,3
FORMULA
Lim_{n->oo} a(n)/10^n = 0.00869419399... (A318645) is the density of e-perfect numbers.
EXAMPLE
Below 10^2 there is only one e-perfect number, A054979(1) = 36, thus a(2) = 1.
MATHEMATICA
fun[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ fun @@@ FactorInteger[n]; c = 0; k = 1; seq={}; Do[ While[ k < 10^n, If[ esigma[k]==2k, c++ ]; k ++]; AppendTo[seq, c], {n, 1, 5}]; seq
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Apr 30 2019
STATUS
approved