cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A327947 #5 Sep 30 2019 20:17:33
%S A327947 24,48,72,96,144,216,240,288,360,480,720,1080,1440,2160,2880,3600,
%T A327947 4320,5040,7200,7560,10080,15120,20160,25200,30240
%N 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.
%C A327947 The nonunitary version of A065218.
%C A327947 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 A327947 24 is the least number which is the sum of its nonunitary divisor, thus a(1) = 24.
%e A327947 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 A327947 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 A327947 Cf. A064591, A064597, A065218, A327945, A327946.
%K A327947 nonn,more
%O A327947 1,1
%A A327947 _Amiram Eldar_, Sep 30 2019