A175592 Numbers n whose prime factors can be partitioned into two disjoint sets whose sums are both (sum of primes dividing n (with repetition))/2.

4, 9, 16, 25, 30, 36, 49, 64, 70, 72, 81, 84, 100, 120, 121, 144, 169, 196, 225, 240, 256, 270, 280, 286, 288, 289, 308, 324, 336, 361, 378, 400, 440, 441, 480, 484, 495, 525, 528, 529, 540, 576, 594, 625, 630, 646, 648, 672, 676, 728, 729, 750, 756, 784

Offset

1,1

Comments

Alternatively, the two sets of prime factors have an equal sum. - Christian N. K. Anderson, Apr 16 2013

Superset of even powers, p^(2*i) where p is a prime number (A056798), and composites thereof. - Christian N. K. Anderson, Apr 16 2013

Links

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Christian N. K. Anderson, Equal sum partitions of prime factors of a(n).

Example

a(1)=4 because 4=2*2 and 2=2, a(2)=9 because 9=3*3 and 3=3, a(3)=16 because 16=2*2*2*2 and 2+2=2+2, a(4)=25 because 25=5*5 and 5=5, a(5)=30 because 30=2*3*5 and 2+3=5.

Prog

(Haskell)
a175592 n = a175592_list !! (n-1)
a175592_list = filter (z 0 0 . a027746_row) $ [1..] 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. A001414, A083207.

Cf. A056798.

Cf. A027746, A221054.

Sequence in context: A266918 A086132 A010433 * A331219 A337534 A126589

Adjacent sequences: A175589 A175590 A175591 * A175593 A175594 A175595

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 20 2010

Extensions

Corrected by Christian N. K. Anderson, Apr 16 2013

Status

approved