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A321206
Exponential pseudoperfect numbers (A318100) that are not e-perfect (A054979).
1
900, 1764, 3600, 4356, 4500, 6084, 6300, 7056, 8100, 8820, 9900, 10404, 11700, 12348, 12996, 15300, 17100, 19044, 19404, 20700, 21780, 22500, 22932, 25200, 26100, 27900, 29988, 30276, 30420, 30492, 31500, 33300, 33516, 34596, 35280, 36900, 38700, 39600, 40572
OFFSET
1,1
COMMENTS
It seems that most of the exponential pseudoperfect numbers are e-perfect. Up to 10^6 there are 9674 exponential pseudoperfect numbers, of them only 984 are not e-perfect.
LINKS
Eric Weisstein's World of Mathematics, e-Divisor
Eric Weisstein's World of Mathematics, e-Perfect Number
MATHEMATICA
dQ[n_, m_] := (n>0&&m>0 &&Divisible[n, m]); expDivQ[n_, d_] := Module[ {ft=FactorInteger[n]}, And@@MapThread[dQ, {ft[[;; , 2]], IntegerExponent[ d, ft[[;; , 1]]]} ]]; eDivs[n_] := Module[ {d=Rest[Divisors[n]]}, Select[ d, expDivQ[n, #]&] ]; esigma[1]=1; esigma[n_] := Total@eDivs[n]; eAbundantQ[n_] := esigma[n] > 2n; a = {}; n = 0; While[Length[a] < 30, n++; If[!eAbundantQ[n], Continue[]]; d = Most[eDivs[n]]; c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; If[c > 0, AppendTo[a, n]]]; a
CROSSREFS
Sequence in context: A129575 A328136 A336254 * A336680 A074853 A162143
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 30 2018
STATUS
approved