

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
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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 112=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 !! (n1)
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. A071139A071147, 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



