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A225495 Numbers having only weak prime factors, cf. A051635.

%I A225495 #7 Mar 17 2018 04:08:09
%S A225495 1,3,7,9,13,19,21,23,27,31,39,43,47,49,57,61,63,69,73,81,83,89,91,93,
%T A225495 103,109,113,117,129,131,133,139,141,147,151,161,167,169,171,181,183,
%U A225495 189,193,199,207,217,219,229,233,241,243,247,249,267,271,273,279
%N A225495 Numbers having only weak prime factors, cf. A051635.
%H A225495 Reinhard Zumkeller, <a href="/A225495/b225495.txt">Table of n, a(n) for n = 1..5000</a>
%F A225495 Multiplicative closure of A051635.
%e A225495 a(10) = 31 = A051635(6);
%e A225495 a(11) = 39 = 3 * 13 = A051635(1) * A051635(3);
%e A225495 a(12) = 43 = A051635(7);
%e A225495 a(13) = 47 = A051635(8);
%e A225495 a(14) = 49 = 7^2 = A051635(2)^2;
%e A225495 a(15) = 57 = 3 * 19 = A051635(1) * A051635(4).
%o A225495 (Haskell)
%o A225495 import Data.Set (singleton, fromList, union, deleteFindMin)
%o A225495 a225495 n = a225495_list !! (n-1)
%o A225495 a225495_list = 1 : h (singleton p) ps [p] where
%o A225495    (p:ps) = a051635_list
%o A225495    h s xs'@(x:xs) ys
%o A225495      | m > x     = h (s `union` (fromList $ map (* x) (1 : ys))) xs ys
%o A225495      | otherwise = m : h (s' `union` (fromList $ map (* m) ys')) xs' ys'
%o A225495      where ys' = m : ys; (m, s') = deleteFindMin s
%Y A225495 Cf. A225493 (strong), A225494 (balanced), A225496 (non-balanced).
%K A225495 nonn
%O A225495 1,2
%A A225495 _Reinhard Zumkeller_, May 09 2013