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%I #5 Sep 30 2019 20:17:33
%S 24,48,72,96,144,216,240,288,360,480,720,1080,1440,2160,2880,3600,
%T 4320,5040,7200,7560,10080,15120,20160,25200,30240
%N 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.
%C The nonunitary version of A065218.
%C The corresponding numbers of ways are 1, 2, 4, 5, 15, 28, 34, 63, 211, 279, 6025, 17436, 187794, 2035726, 5965563, 36449982, 250420995, 3426156924, 8991176276, 37016127059, 6770551810345, 1095548357870254, 13524344273940115, 604532928571438678, 33370817837127087825, ...
%e 24 is the least number which is the sum of its nonunitary divisor, thus a(1) = 24.
%e 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.
%t 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
%Y Cf. A064591, A064597, A065218, A327945, A327946.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Sep 30 2019
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