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.

A334407 Numbers k whose divisors can be partitioned into two disjoint sets with equal sum, such that if d is in one set, then k/d is in the other set.

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%I A334407 #10 Apr 28 2020 05:56:28
%S A334407 60,140,160,168,180,216,220,252,260,300,312,340,360,380,396,420,432,
%T A334407 460,462,480,500,504,520,540,580,600,616,620,624,630,660,672,684,720,
%U A334407 728,740,756,780,792,810,820,840,858,860,864,870,924,936,940,960,990,1008,1020
%N A334407 Numbers k whose divisors can be partitioned into two disjoint sets with equal sum, such that if d is in one set, then k/d is in the other set.
%H A334407 Amiram Eldar, <a href="/A334407/b334407.txt">Table of n, a(n) for n = 1..1000</a>
%e A334407 60 is a term since its set of divisors can be partitioned into two disjoint subsets: {1, 6, 12, 15, 20, 30} and {60, 10, 5, 4, 3, 2} = {60/1, 60/6, 60/12, 60/15, 60/20, 60/30} with the equal sum of 84, and with no pair of complementary divisors (d, 60/d) in the same subset.
%t A334407 seqQ[n_] := Module[{d = Divisors[n]}, nd = Length[d]; If[OddQ[nd], False, divpairs = d[[-1 ;; nd/2 + 1 ;; -1]] - d[[1 ;; nd/2]]; sd = Plus @@ divpairs; If[OddQ[sd], False, SeriesCoefficient[Series[Product[1 + x^divpairs[[i]], {i, Length[divpairs]}], {x, 0, sd/2}], sd/2] > 0]]]; Select[Range[1000], seqQ]
%Y A334407 Subsequence of A083207.
%K A334407 nonn
%O A334407 1,1
%A A334407 _Amiram Eldar_, Apr 27 2020