A321206 Exponential pseudoperfect numbers (A318100) that are not e-perfect (A054979).

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

Amiram Eldar, Table of n, a(n) for n = 1..1000

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

Cf. A054979, A318100.

Sequence in context: A129575 A328136 A336254 * A336680 A074853 A162143

Adjacent sequences: A321203 A321204 A321205 * A321207 A321208 A321209

Keyword

nonn

Author

Amiram Eldar, Oct 30 2018

Status

approved