A327947 Nonunitary pseudoperfect numbers (A327945) that equal to the sum of a subset of their nonunitary divisors in more ways than any smaller nonunitary pseudoperfect number.
24, 48, 72, 96, 144, 216, 240, 288, 360, 480, 720, 1080, 1440, 2160, 2880, 3600, 4320, 5040, 7200, 7560, 10080, 15120, 20160, 25200, 30240
Offset: 1
Examples
24 is the least number which is the sum of its nonunitary divisor, thus a(1) = 24. 48 is the least number which is the sum of a subset of its nonunitary divisor in two ways: 24 + 12 + 8 + 4 and 24 + 12 + 8 + 4 + 2, thus a(2) = 48.
Programs
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Mathematica
nudiv[n_] := Module[{d = Divisors[n]}, Select[d, GCD[#, n/#] > 1 &]]; s = {}; cm = 0; Do[d = nudiv[n]; If[Total[d] < n, Continue[]]; c = SeriesCoefficient[ Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; If[c > cm, cm = c; AppendTo[s, n]], {n, 1, 1000}]; s
Comments