A302035 a(1) = 0, for n > 1, a(n) = A001511(A260739(n)); Number of instances of (the smallest) Ludic factor A272565(n) in n.

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, 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, 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

Offset

1,4

Comments

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10105

Index entries for sequences generated by sieves

Formula

a(1) = 0; for n > 1, a(n) = A001511(A260739(n)).

For n > 1, a(n) = A302025(A067029(A302026(n))).

Crossrefs

Cf. A001511, A003309, A255127, A260739, A302025, A302026, A302032, A302034.

Cf. also A067029, A302045.

Sequence in context: A087179 A290109 A302045 * A307907 A362333 A371148

Adjacent sequences: A302032 A302033 A302034 * A302036 A302037 A302038

Keyword

nonn

Author

Antti Karttunen, Apr 01 2018

Status

approved