OFFSET
1,1
COMMENTS
From Christian N. K. Anderson, Apr 16 2013: (Start)
Alternatively, the two sets of prime factors have an equal sum.
Superset of even powers, p^(2*i) where p is a prime number (A056798), and composites thereof. (End)
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.
MAPLE
Primefactors := proc(n) local F, f, i; F := [];
for f in ifactors(n)[2] do
for i from 1 to f[2] do
F := [op(F), f[1]]
od od; F end:
isPrimeZumkeller := proc(n) option remember; local s, p, i, P;
s := add(Primefactors(n)); # A001414
if s::odd or s = 0 then return false fi;
P := mul(1 + x^i, i in Primefactors(n));
is(0 < coeff(P, x, s/2)) end:
select(isPrimeZumkeller, [seq(1..800)]); # Peter Luschny, Oct 21 2024
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
KEYWORD
nonn,changed
AUTHOR
Juri-Stepan Gerasimov, Jul 20 2010
EXTENSIONS
Corrected by Christian N. K. Anderson, Apr 16 2013
STATUS
approved