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 A221054 Numbers whose distinct prime factors can be partitioned into two equal sums. 3
 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, 2160, 2240, 2250, 2288, 2310, 2400, 2430, 2450, 2584, 2700, 2800, 2880, 3000, 3135 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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). Divergences become more common thereafter, including 102 of the first 500 terms. As with the two sequences above, this is a superset of 2*product of twin primes (A037074). LINKS Christian N. K. Anderson, Table of n, a(n) for n = 1..1000 Christian N. K. Anderson, Partitions of distinct prime factors of the first 1000 terms. PROG (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 CROSSREFS Cf. A175592 (multiplicity of prime factors allowed). Cf. A071139-A071147, especially A071140. Cf. A008472, A037074. Cf. A027748, A005843, A083207. Sequence in context: A212666 A291046 A071140 * A074915 A073461 A222618 Adjacent sequences:  A221051 A221052 A221053 * A221055 A221056 A221057 KEYWORD nonn AUTHOR Kevin L. Schwartz and Christian N. K. Anderson, Apr 15 2013 STATUS approved

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Last modified April 4 05:15 EDT 2020. Contains 333212 sequences. (Running on oeis4.)