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%I #46 Apr 08 2018 20:08:49
%S 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,
%T 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,
%U 3,2,5,2,67,2,3,2,71,2,13,2,3,2,77,2,5,2,3
%N Ludic factor of n.
%C 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.
%C 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
%H Max Barrentine, <a href="/A272565/b272565.txt">Table of n, a(n) for n = 1..10000</a>
%H OEIS Wiki, <a href="http://oeis.org/wiki/Ludic_numbers">Ludic numbers</a>.
%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F From _Antti Karttunen_, Sep 11 2016: (Start)
%F a(n) = A003309(1+A260738(n)).
%F For all n >= 1, a(A276347(n)) = A020639(A276347(n)).
%F (End).
%o (Scheme) (define (A272565 n) (A003309 (+ 1 (A260738 n)))) ;; _Antti Karttunen_, Sep 11 2016
%Y Cf. A003309, A020639, A027748, A192607, A255127, A260738, A276440, A276568, A276569, A302032.
%Y Cf. A276347, A276447, A276448 (ludic factor is equal, less than or greater than the smallest prime factor).
%Y Cf. A260739 (ordinal transform), A302036 (numbers with all Ludic factors equal).
%Y Cf. A264940 (analogous version for lucky numbers).
%K nonn
%O 1,2
%A _Max Barrentine_, May 09 2016
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