A327715 a(0) = 0; for n >= 1, a(n) = 1 + a(n-A009191(n)).

0, 1, 1, 2, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 8, 9, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 19, 20, 20, 21, 19, 20, 20, 20, 21, 22, 22, 23, 23, 24, 24, 25, 20, 21, 21, 21, 22, 23, 23, 24, 25, 26

Offset: 0

Author

Ctibor O. Zizka, Sep 23 2019

Keywords

• nonn

Comments

Number of steps needed to reach zero when starting from k = n and repeatedly applying the map that replaces k with k - gcd(k,d(k)), where d(k) is the number of divisors of k (A000005).

Empirically: n/log(n) <= a(n) <= n/log(n) + 2*log(n).

Examples

			a(6) = 1 + a(6-gcd(6,4)) = 1 + a(4) = 2 + a(4-gcd(4,3)) = 2 + a(3) = 3 + a(3-gcd(3,2)) = 3 + a(2) = 4 + a(2-gcd(2,2)) = 4 + a(0) = 4.
		

Crossrefs

Cf. A000005, A009191, A155043.

Programs

PARI

a(n) = if (n==0, 0, 1 + a(n - gcd(n, numdiv(n)))); \\ Michel Marcus, Sep 25 2019