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A225496 Numbers having no balanced prime factors, cf. A006562.

%I A225496 #4 May 09 2013 11:01:12
%S A225496 1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24,26,27,28,29,31,
%T A225496 32,33,34,36,37,38,39,41,42,43,44,46,47,48,49,51,52,54,56,57,58,59,61,
%U A225496 62,63,64,66,67,68,69,71,72,73,74,76,77,78,79,81,82,83,84
%N A225496 Numbers having no balanced prime factors, cf. A006562.
%C A225496 a(n) = A047201(n) for n <= 42.
%H A225496 Reinhard Zumkeller, <a href="/A225496/b225496.txt">Table of n, a(n) for n = 1..5000</a>
%F A225496 Multiplicative closure of A178943; a(n) mod A006562(k) > 0 for all k.
%e A225496 a(40) = 49 = 7^2 = A178943(3)^2;
%e A225496 a(41) = 51 = 3 * 17 = A178943(2) * A178943(6);
%e A225496 a(42) = 52 = 2^2 * 13 = A178943(1)^2 * A178943(5);
%e A225496 a(43) = 54 = 2 * 3^3 = A178943(1) * A178943(2)^3;
%e A225496 a(44) = 56 = 2^3 * 7 = A178943(1)^3 * A178943(3);
%e A225496 a(45) = 57 = 3 * 19 = A178943(2) * A178943(7).
%o A225496 (Haskell)
%o A225496 import Data.Set (singleton, fromList, union, deleteFindMin)
%o A225496 a225496 n = a225496_list !! (n-1)
%o A225496 a225496_list = 1 : h (singleton p) ps [p] where
%o A225496    (p:ps) = a178943_list
%o A225496    h s xs'@(x:xs) ys
%o A225496      | m > x     = h (s `union` (fromList $ map (* x) (1 : ys))) xs ys
%o A225496      | otherwise = m : h (s' `union` (fromList $ map (* m) ys')) xs' ys'
%o A225496      where ys' = m : ys; (m, s') = deleteFindMin s
%Y A225496 Cf. A225493 (strong), A225494 (balanced), A225495 (weak).
%K A225496 nonn
%O A225496 1,2
%A A225496 _Reinhard Zumkeller_, May 09 2013