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

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, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84

Offset: 1

Author

Reinhard Zumkeller, May 09 2013

Keywords

• nonn

Comments

a(n) = A047201(n) for n <= 42.

Examples

			a(40) = 49 = 7^2 = A178943(3)^2;
a(41) = 51 = 3 * 17 = A178943(2) * A178943(6);
a(42) = 52 = 2^2 * 13 = A178943(1)^2 * A178943(5);
a(43) = 54 = 2 * 3^3 = A178943(1) * A178943(2)^3;
a(44) = 56 = 2^3 * 7 = A178943(1)^3 * A178943(3);
a(45) = 57 = 3 * 19 = A178943(2) * A178943(7).
		

Links

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

Crossrefs

Cf. A225493 (strong), A225494 (balanced), A225495 (weak).

Programs

Haskell

import Data.Set (singleton, fromList, union, deleteFindMin)
a225496 n = a225496_list !! (n-1)
a225496_list = 1 : h (singleton p) ps [p] where
   (p:ps) = a178943_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 A178943; a(n) mod A006562(k) > 0 for all k.