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

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

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 * A365795 A074915 A073461

Adjacent sequences: A221051 A221052 A221053 * A221055 A221056 A221057

Keyword

nonn

Author

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

Status

approved