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

1,2

Comments

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

Links

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

Formula

Multiplicative closure of A178943; a(n) mod A006562(k) > 0 for all k.

Example

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).

Prog

(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

Crossrefs

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

Sequence in context: A039116 A330002 A047201 * A261189 A023721 A087066

Adjacent sequences: A225493 A225494 A225495 * A225497 A225498 A225499

Keyword

nonn

Author

Reinhard Zumkeller, May 09 2013

Status

approved