%I #17 Apr 23 2013 11:13:55

%S 30,60,70,90,120,140,150,180,240,270,280,286,300,350,360,450,480,490,

%T 540,560,572,600,646,700,720,750,810,900,960,980,1080,1120,1144,1200,

%U 1292,1350,1400,1440,1500,1620,1750,1798,1800,1920,1960,2160,2240,2250,2288,2310,2400,2430,2450,2584,2700,2800,2880,3000,3135

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

%C This sequence is nearly identical to A071140 and Lagneau's proposed definition of the same. The first divergence occurs at a(50)=2310, whose prime factors 2+5+7=3+11; however 2+3+5+7+11=28 is not divisible by 11 (def 1), nor is 11-2=3+5+7 (def 2).

%C Divergences become more common thereafter, including 102 of the first 500 terms.

%C As with the two sequences above, this is a superset of 2*product of twin primes (A037074).

%H Christian N. K. Anderson, <a href="/A221054/b221054.txt">Table of n, a(n) for n = 1..1000</a>

%H Christian N. K. Anderson, <a href="/A221054/a221054.txt">Partitions of distinct prime factors</a> of the first 1000 terms.

%o (Haskell)

%o a221054 n = a221054_list !! (n-1)

%o a221054_list = filter (z 0 0 . a027748_row) $ tail a005843_list where

%o z u v [] = u == v

%o z u v (p:ps) = z (u + p) v ps || z u (v + p) ps

%o -- _Reinhard Zumkeller_, Apr 18 2013

%Y Cf. A175592 (multiplicity of prime factors allowed).

%Y Cf. A071139-A071147, especially A071140.

%Y Cf. A008472, A037074.

%Y Cf. A027748, A005843, A083207.

%K nonn

%O 1,1

%A _Kevin L. Schwartz_ and _Christian N. K. Anderson_, Apr 15 2013