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A321145 Exponential pseudoperfect numbers (A318100) equal to the sum of a subset of their proper exponential divisors in a single way. 1
36, 180, 252, 396, 468, 612, 684, 828, 1044, 1116, 1260, 1332, 1476, 1548, 1692, 1800, 1908, 1980, 2124, 2196, 2340, 2412, 2556, 2628, 2700, 2772, 2844, 2988, 3060, 3204, 3276, 3420, 3492, 3636, 3708, 3852, 3924, 4068, 4140, 4284, 4500, 4572, 4716, 4788, 4932 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The exponential version of A064771.

LINKS

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, e-Divisor

Eric Weisstein's World of Mathematics, e-Perfect Number

EXAMPLE

4500 is in the sequence since its proper exponential divisors are 30, 60, 90, 180, 750, 1500, 2250 and {750, 1500, 2250} is the only subset that sums to 4500.

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]; eDeficientQ[n_] := esigma[n] < 2n; a = {}; n = 0; While[Length[a] < 30, n++; If[eDeficientQ[n], Continue[]]; d = Most[eDivs[n]]; c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; If[c == 1, AppendTo[a, n]]]; a

CROSSREFS

Cf. A064771, A295829, A295830, A318100.

Sequence in context: A127657 A318100 A335218 * A054979 A335219 A102949

Adjacent sequences:  A321142 A321143 A321144 * A321146 A321147 A321148

KEYWORD

nonn

AUTHOR

Amiram Eldar, Oct 28 2018

STATUS

approved

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Last modified July 5 03:37 EDT 2020. Contains 335459 sequences. (Running on oeis4.)