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A225494 Numbers having only balanced prime factors, cf. A006562.

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