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

1, 3, 7, 9, 13, 19, 21, 23, 27, 31, 39, 43, 47, 49, 57, 61, 63, 69, 73, 81, 83, 89, 91, 93, 103, 109, 113, 117, 129, 131, 133, 139, 141, 147, 151, 161, 167, 169, 171, 181, 183, 189, 193, 199, 207, 217, 219, 229, 233, 241, 243, 247, 249, 267, 271, 273, 279

Offset: 1

Author

Reinhard Zumkeller, May 09 2013

Keywords

• nonn

Examples

			a(10) = 31 = A051635(6);
a(11) = 39 = 3 * 13 = A051635(1) * A051635(3);
a(12) = 43 = A051635(7);
a(13) = 47 = A051635(8);
a(14) = 49 = 7^2 = A051635(2)^2;
a(15) = 57 = 3 * 19 = A051635(1) * A051635(4).
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A225493 (strong), A225494 (balanced), A225496 (non-balanced).

Programs

Haskell

import Data.Set (singleton, fromList, union, deleteFindMin)
a225495 n = a225495_list !! (n-1)
a225495_list = 1 : h (singleton p) ps [p] where
   (p:ps) = a051635_list
   h s xs'@(x:xs) ys
     | m > x     = h (s `union` (fromList $ map (* x) (1 : ys))) xs ys
     | otherwise = m : h (s' `union` (fromList $ map (* m) ys')) xs' ys'
     where ys' = m : ys; (m, s') = deleteFindMin s

Formula

Multiplicative closure of A051635.