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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 (list; graph; refs; listen; history; text; internal format)
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 16-2 = 14 is 7,

- the greatest prime factor of 14-7 = 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

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Last modified January 26 23:05 EST 2020. Contains 331289 sequences. (Running on oeis4.)