A297025 Number of iterations of A220096 required to reach 0 starting from n.

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

Offset: 0

Author

Peter Kagey and Alec Jones, Dec 24 2017

Keywords

• nonn

Comments

Records occur at indices 0, 1, 2, 3, 5, 7, 11, 22, 23, 46, 47, 94, ... (see A297026).

Examples

			For n = 14, a(14) = 6 because six iterations are required to reach zero:
A220096(14) = 7,
A220096(7)  = 6,
A220096(6)  = 3,
A220096(3)  = 2,
A220096(2)  = 1, and
A220096(1)  = 0.
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A220096. Positions of records at A297026.

Cf. A056792, A061282, A260112.

Programs

Mathematica

g[n_Integer] := If[n == 1, 0, Block[{fi = FactorInteger@ n}, If[Plus @@ (Last@# & /@ FactorInteger@n) == 1, n -1, n/fi[[1, 1]] ]]]; f[n_] := Length@ NestWhileList[g, n, # > 0 &] -1; Array[f, 86, 0] (* Robert G. Wilson v, Dec 24 2017 *)

PARI

f(n) = if (n==1, 0, isprime(n), n-1, my(d=divisors(n)); d[#d-1]);
a(n) = my(nb = 0); while (n, n = f(n); nb++); nb; \\ Michel Marcus, Dec 24 2017