A264940 Lucky factor of n.

0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 9, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 15, 2, 9, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 21, 2

Offset

1,2

Comments

This sequence is analogous to the smallest prime factor of n (A020639). If n is lucky, a(n)=0; if n is unlucky, a(n) is the number that rejects n from the lucky number sieve. This is 2 for even numbers, and a lucky number >= 3 for odd unlucky numbers.

Links

Max Barrentine, Table of n, a(n) for n = 1..10000

Formula

From Antti Karttunen, Sep 11 2016: (Start)

If A145649(n) = 1 [when n is lucky], a(n) = 0, else if n is even, a(n) = 2, otherwise a(n) = A000959(A265859(n)) = A000959(A260438(n)).

For n >= 2, a(A219178(n)) = A000959(n).

(End)

Prog

(Scheme) (define (A264940 n) (if (= 1 (A145649 n)) 0 (if (even? n) 2 (A000959 (A260438 n))))) ;; Antti Karttunen, Sep 11 2016

Crossrefs

Cf. A000959, A050505, A145649, A219178, A255543, A255545, A260438, A265859.

Cf. A020639, A271419 (somewhat analogous sequences).

Sequence in context: A202036 A246752 A246650 * A272800 A104513 A357618

Adjacent sequences: A264937 A264938 A264939 * A264941 A264942 A264943

Keyword

nonn

Author

Max Barrentine, Dec 09 2015

Extensions

Formula corrected and comment clarified by Antti Karttunen, Sep 11 2016

Status

approved