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%I #7 Mar 17 2018 04:08:06
%S 1,5,25,53,125,157,173,211,257,263,265,373,563,593,607,625,653,733,
%T 785,865,947,977,1055,1103,1123,1187,1223,1285,1315,1325,1367,1511,
%U 1747,1753,1865,1907,2287,2417,2677,2809,2815,2903,2963,2965,3035,3125,3265,3307
%N Numbers having only balanced prime factors, cf. A006562.
%H Reinhard Zumkeller, <a href="/A225494/b225494.txt">Table of n, a(n) for n = 1..5000</a>
%F Multiplicative closure of A006562.
%o (Haskell)
%o import Data.Set (singleton, fromList, union, deleteFindMin)
%o a225494 n = a225494_list !! (n-1)
%o a225494_list = 1 : h (singleton p) ps [p] where
%o (p:ps) = a006562_list
%o h s xs'@(x:xs) ys
%o | m > x = h (s `union` (fromList $ map (* x) (1 : ys))) xs ys
%o | otherwise = m : h (s' `union` (fromList $ map (* m) ys')) xs' ys'
%o where ys' = m : ys; (m, s') = deleteFindMin s
%Y Cf. A225493 (strong), A225495 (weak), A225496 (non-balanced).
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, May 09 2013
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