

A309892


a(0) = 0, a(1) = 1, and for any n > 1, a(n) is the number of iterations of the map x > x  gpf(x) (where gpf(x) denotes the greatest prime factor of x) required to reach 0 starting from n.


2



0, 1, 1, 1, 2, 1, 2, 1, 3, 3, 2, 1, 4, 1, 2, 3, 3, 1, 4, 1, 4, 3, 2, 1, 4, 5, 2, 5, 4, 1, 6, 1, 7, 3, 2, 5, 4, 1, 2, 3, 6, 1, 6, 1, 4, 7, 2, 1, 8, 7, 8, 3, 4, 1, 4, 5, 8, 3, 2, 1, 6, 1, 2, 9, 3, 5, 6, 1, 4, 3, 10, 1, 4, 1, 2, 11, 4, 7, 6, 1, 12, 7, 2, 1, 8, 5
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OFFSET

0,5


COMMENTS

This sequence is similar to A175126: here we subtract the greatest prime factor, there the least prime factor.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537


FORMULA

a(n) <= n / A006530(n) for any n > 0.
a(n) = n if n <= 1, for n >= 2, a(n) = 1+a(A076563(n)).  Antti Karttunen, Aug 22 2019


EXAMPLE

For n = 16:
 the greatest prime factor of 16 is 2,
 the greatest prime factor of 162 = 14 is 7,
 the greatest prime factor of 147 = 7 is 7,
 7  7 = 0,
 hence a(16) = 3.


PROG

(PARI) a(n) = for (k=0, oo, if (n==0, return (k), n==1, n, my (f=factor(n)); n=f[#f~, 1]))


CROSSREFS

Cf. A006530, A052126, A076563, A175126.
Sequence in context: A322866 A328847 A331175 * A078899 A055172 A187445
Adjacent sequences: A309889 A309890 A309891 * A309893 A309894 A309895


KEYWORD

nonn


AUTHOR

Rémy Sigrist, Aug 21 2019


STATUS

approved



