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

1, 30, 60, 70, 90, 120, 140, 150, 180, 240, 270, 280, 286, 300, 350, 360, 450, 480, 490, 540, 560, 572, 600, 646, 700, 720, 750, 810, 900, 960, 980, 1080, 1120, 1144, 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

Offset: 1

Author

Kevin L. Schwartz and Christian N. K. Anderson, Apr 15 2013

Keywords

• nonn

Comments

This is a superset of 2*product of twin primes, A071142.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Christian N. K. Anderson, Table of n, a(n), and equal sums of factors for n=1..10000

Crossrefs

Cf. A175592 (multiplicity of prime factors allowed).

Cf. A071139-A071147, especially A071140.

Cf. A008472, A037074, A071142.

Cf. A027748, A005843, A083207.

Programs

Haskell

a221054 n = a221054_list !! (n-1)
a221054_list = filter (z 0 0 . a027748_row) $ tail a005843_list where
   z u v []     = u == v
   z u v (p:ps) = z (u + p) v ps || z u (v + p) ps
-- Reinhard Zumkeller, Apr 18 2013

Mathematica

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 *)

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

Extensions

Missing terms inserted by Michel Marcus, May 31 2025