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%I #25 Mar 15 2016 08:00:47
%S 4,9,16,25,30,36,49,64,70,72,81,84,100,120,121,144,169,196,225,240,
%T 256,270,280,286,288,289,308,324,336,361,378,400,440,441,480,484,495,
%U 525,528,529,540,576,594,625,630,646,648,672,676,728,729,750,756,784
%N Numbers n whose prime factors can be partitioned into two disjoint sets whose sums are both (sum of primes dividing n (with repetition))/2.
%C Alternatively, the two sets of prime factors have an equal sum. - _Christian N. K. Anderson_, Apr 16 2013
%C Superset of even powers, p^(2*i) where p is a prime number (A056798), and composites thereof. - _Christian N. K. Anderson_, Apr 16 2013
%H Christian N. K. Anderson, <a href="/A175592/b175592.txt">Table of n, a(n) for n = 1..10000</a>
%H Christian N. K. Anderson, <a href="/A175592/a175592_1.txt">Equal sum partitions</a> of prime factors of a(n).
%e 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.
%o (Haskell)
%o a175592 n = a175592_list !! (n-1)
%o a175592_list = filter (z 0 0 . a027746_row) $ [1..] 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. A001414, A083207.
%Y Cf. A056798.
%Y Cf. A027746, A221054.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Jul 20 2010
%E Corrected by _Christian N. K. Anderson_, Apr 16 2013
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