%I #8 Mar 17 2018 04:08:03

%S 1,11,17,29,37,41,59,67,71,79,97,101,107,121,127,137,149,163,179,187,

%T 191,197,223,227,239,251,269,277,281,289,307,311,319,331,347,367,379,

%U 397,407,419,431,439,451,457,461,479,487,493,499,521,541,557,569,587

%N Numbers having only strong prime factors, cf. A051634.

%H Reinhard Zumkeller, <a href="/A225493/b225493.txt">Table of n, a(n) for n = 1..5000</a>

%F Multiplicative closure of A051634.

%o (Haskell)

%o import Data.Set (singleton, fromList, union, deleteFindMin)

%o a225493 n = a225493_list !! (n-1)

%o a225493_list = 1 : h (singleton p) ps [p] where

%o (p:ps) = a051634_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. A225494 (balanced), A225495 (weak), A225496 (non-balanced).

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, May 09 2013