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A221054 Numbers whose distinct prime factors can be partitioned into two equal sums.

%I A221054 #35 Jun 18 2025 00:58:13
%S A221054 1,30,60,70,90,120,140,150,180,240,270,280,286,300,350,360,450,480,
%T A221054 490,540,560,572,600,646,700,720,750,810,900,960,980,1080,1120,1144,
%U A221054 1200,1292,1350,1400,1440,1500,1620,1750,1798,1800,1920,1960,2145,2160,2240,2250,2288,2310,2400,2430,2450,2584,2700,2730,2800,2880,3000,3135
%N A221054 Numbers whose distinct prime factors can be partitioned into two equal sums.
%C A221054 This is a superset of 2*product of twin primes, A071142.
%H A221054 Alois P. Heinz, <a href="/A221054/b221054.txt">Table of n, a(n) for n = 1..10000</a>
%H A221054 Christian N. K. Anderson, <a href="/A221054/a221054_1.txt">Table of n, a(n), and equal sums of factors for n=1..10000</a>
%t A221054 q[n_] := Module[{p = FactorInteger[n][[;; , 1]], sum, x}, sum = Total[p]; EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, p}], x][[1 + sum/2]] > 0]; Select[Range[3200], q] (* _Amiram Eldar_, May 31 2025 *)
%o A221054 (Haskell)
%o A221054 a221054 n = a221054_list !! (n-1)
%o A221054 a221054_list = filter (z 0 0 . a027748_row) $ tail a005843_list where
%o A221054    z u v []     = u == v
%o A221054    z u v (p:ps) = z (u + p) v ps || z u (v + p) ps
%o A221054 -- _Reinhard Zumkeller_, Apr 18 2013
%o A221054 (PARI) isok(k) = my(f=factor(k), nb=#f~); for (i=0,2^nb-1, my(v=Vec(Vecrev(binary(i)), nb)); if (sum(k=1, nb, if (v[k], f[k,1])) == sum(k=1, nb, if (!v[k], f[k,1])), return(1));); \\ _Michel Marcus_, May 31 2025
%Y A221054 Cf. A175592 (multiplicity of prime factors allowed).
%Y A221054 Cf. A071139-A071147, especially A071140.
%Y A221054 Cf. A008472, A037074, A071142.
%Y A221054 Cf. A027748, A005843, A083207.
%K A221054 nonn
%O A221054 1,2
%A A221054 _Kevin L. Schwartz_ and _Christian N. K. Anderson_, Apr 15 2013
%E A221054 Missing terms inserted by _Michel Marcus_, May 31 2025