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

0,3

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A220096. Positions of records at A297026.

Cf. A056792, A061282, A260112.

Sequence in context: A317658 A277615 A064066 * A325134 A218007 A060607

Adjacent sequences: A297022 A297023 A297024 * A297026 A297027 A297028

Keyword

nonn

Author

Peter Kagey and Alec Jones, Dec 24 2017

Status

approved