A272565 Ludic factor of n.

1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 5, 2, 3, 2, 23, 2, 25, 2, 3, 2, 29, 2, 7, 2, 3, 2, 5, 2, 37, 2, 3, 2, 41, 2, 43, 2, 3, 2, 47, 2, 5, 2, 3, 2, 53, 2, 11, 2, 3, 2, 7, 2, 61, 2, 3, 2, 5, 2, 67, 2, 3, 2, 71, 2, 13, 2, 3, 2, 77, 2, 5, 2, 3

Offset

1,2

Comments

This sequence is somewhat analogous to the smallest prime factor of n (A020639). However, each natural number has only one ludic factor, because once it is crossed off in the k-th step of the sieve process, it is not a member of the terms considered in the (k+1)-th step.

On the other hand, by iteratively invoking A302032 it is possible to factor n to its constituent "Ludic factors", with each natural number having a unique such decomposition, analogous to prime factorization of n. See comments and examples given in A302032. - Antti Karttunen, Apr 08 2018

Links

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

OEIS Wiki, Ludic numbers.

Index entries for sequences generated by sieves

Formula

From Antti Karttunen, Sep 11 2016: (Start)

a(n) = A003309(1+A260738(n)).

For all n >= 1, a(A276347(n)) = A020639(A276347(n)).

(End).

Prog

(Scheme) (define (A272565 n) (A003309 (+ 1 (A260738 n)))) ;; Antti Karttunen, Sep 11 2016

Crossrefs

Cf. A003309, A020639, A027748, A192607, A255127, A260738, A276440, A276568, A276569, A302032.

Cf. A276347, A276447, A276448 (ludic factor is equal, less than or greater than the smallest prime factor).

Cf. A260739 (ordinal transform), A302036 (numbers with all Ludic factors equal).

Cf. A264940 (analogous version for lucky numbers).

Sequence in context: A085308 A209190 A086286 * A135679 A092028 A020639

Adjacent sequences: A272562 A272563 A272564 * A272566 A272567 A272568

Keyword

nonn

Author

Max Barrentine, May 09 2016

Status

approved