A323076 Number of iterations of map x -> 1+(x-(largest divisor d < x)), starting from x=n, needed to reach a fixed point, which is always either a prime or 1.

0, 0, 0, 1, 0, 2, 0, 1, 1, 3, 0, 1, 0, 2, 1, 2, 0, 4, 0, 1, 2, 2, 0, 1, 3, 3, 1, 2, 0, 3, 0, 1, 1, 5, 1, 1, 0, 2, 2, 3, 0, 3, 0, 1, 1, 2, 0, 4, 1, 4, 2, 2, 0, 3, 2, 1, 3, 4, 0, 1, 0, 2, 1, 2, 1, 6, 0, 2, 1, 2, 0, 1, 0, 3, 3, 3, 1, 4, 0, 1, 3, 4, 0, 1, 2, 2, 1, 2, 0, 3, 1, 1, 2, 5, 2, 2, 0, 5, 1, 3, 0, 3, 0, 1, 1

Offset: 1

Author

Antti Karttunen, Jan 04 2019

Keywords

• nonn

Comments

Differs from A064918 at n = 25, 48, 51, 69, 75, 81, 85, 94, 95, 99, 100, 111, 115, 121, ...

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20669
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A060681, A064918, A323075 (the fixed points reached), A323077, A323079.

Cf. also A039651.

Programs

Mathematica

{0}~Join~Array[-2 + Length@ NestWhileList[1 + (# - Divisors[#][[-2]]) &, #, UnsameQ, All] &, 104, 2] (* Michael De Vlieger, Jan 04 2019 *)

PARI

A060681(n) = (n-if(1==n,n,n/vecmin(factor(n)[,1])));
A323076(n) = { my(nn = 1+A060681(n)); if(nn==n,0,1+A323076(nn)); };

Formula

If n == (1+A060681(n)), then a(n) = 0, otherwise a(n) = 1 + a(1+A060681(n)).