This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A302035 #16 Apr 06 2018 10:16:01 %S A302035 0,1,1,2,1,1,1,3,2,1,1,2,1,1,1,4,1,1,2,2,3,1,1,3,1,1,1,2,1,1,2,5,2,1, %T A302035 1,2,1,1,1,3,1,1,1,2,4,1,1,4,3,1,1,2,1,1,2,3,2,1,1,2,1,1,1,6,1,1,1,2, %U A302035 3,1,1,3,2,1,1,2,1,1,2,4,2,1,1,2,3,1,1,3,1,1,1,2,5,1,1,5,1,1,1,2,2,1,1,3,2 %N A302035 a(1) = 0, for n > 1, a(n) = A001511(A260739(n)); Number of instances of (the smallest) Ludic factor A272565(n) in n. %C A302035 An A067029 analog for "Ludic factorization": iterating the map n -> A302034(n) until 1 is reached, and taking the Ludic factor (A272565) of each term gives a sequence of distinct Ludic numbers (A003309) in ascending order, while applying this function (A302035) to those terms gives the corresponding "exponents" of those Ludic factors, that is, the count of consecutive occurrences of each when iterating the map n -> A302032(n), which gives the same factors with repetitions. Permutation pair A302025/A302026 maps between the Ludic factorization and the ordinary prime factorization of n. See also comments and examples in A302032. %H A302035 Antti Karttunen, <a href="/A302035/b302035.txt">Table of n, a(n) for n = 1..10105</a> %H A302035 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a> %F A302035 a(1) = 0; for n > 1, a(n) = A001511(A260739(n)). %F A302035 For n > 1, a(n) = A302025(A067029(A302026(n))). %Y A302035 Cf. A001511, A003309, A255127, A260739, A302025, A302026, A302032, A302034. %Y A302035 Cf. also A067029, A302045. %K A302035 nonn %O A302035 1,4 %A A302035 _Antti Karttunen_, Apr 01 2018