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

1, 5, 25, 53, 125, 157, 173, 211, 257, 263, 265, 373, 563, 593, 607, 625, 653, 733, 785, 865, 947, 977, 1055, 1103, 1123, 1187, 1223, 1285, 1315, 1325, 1367, 1511, 1747, 1753, 1865, 1907, 2287, 2417, 2677, 2809, 2815, 2903, 2963, 2965, 3035, 3125, 3265, 3307

Offset: 1

Author

Reinhard Zumkeller, May 09 2013

Keywords

• nonn

Links

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

Crossrefs

Cf. A225493 (strong), A225495 (weak), A225496 (non-balanced).

Programs

Haskell

import Data.Set (singleton, fromList, union, deleteFindMin)
a225494 n = a225494_list !! (n-1)
a225494_list = 1 : h (singleton p) ps [p] where
   (p:ps) = a006562_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 A006562.