

A225496


Numbers having no balanced prime factors, cf. A006562.


6



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
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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 !! (n1)
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: A020656 A039116 A047201 * A261189 A023721 A087066
Adjacent sequences: A225493 A225494 A225495 * A225497 A225498 A225499


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, May 09 2013


STATUS

approved



