A075661 Let f(n) = lcd(n)-lpf(n), where lcd(n) is the largest common difference between consecutive divisors of n (ordered by size) and lpf(n) is the largest prime factor of n. Sequence gives number of iterations for f(n) to reach 0 or -1.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 3, 3, 1, 3, 2, 1, 2, 1, 2, 2, 1, 3, 3, 1, 1, 2, 3, 1, 2, 1, 2, 4, 1, 1, 3, 4, 3, 2, 2, 1, 4, 3, 3, 2, 1, 1, 4, 1, 1, 4, 3, 3, 2, 1, 2, 2, 3, 1, 3, 1, 1, 5, 2, 4, 2, 1, 4, 3, 1, 1, 4, 3, 1, 2, 3, 1, 4, 4, 2, 2, 1, 3, 5, 1, 3, 4, 5

Offset

1,8

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Jason Earls, Smarandache iterations of the first kind on functions involving divisors and prime factors, in Smarandache Notions Journal (2004), Vol. 14.1, pp 259-264.

Example

a(24)=3 because 24 -> 9 -> 3 -> -1.

Mathematica

Array[-1 + Length@ NestWhileList[Function[n, Max@ Differences@ # - SelectFirst[Reverse@ #, PrimeQ] &@ Divisors[n]], #, # > 0 &] &, 100] (* Michael De Vlieger, Mar 28 2018 *)

Crossrefs

Cf. A074348.

Sequence in context: A202205 A336123 A353849 * A206829 A319694 A335641

Adjacent sequences: A075658 A075659 A075660 * A075662 A075663 A075664

Keyword

nonn

Author

Jason Earls, Sep 23 2002

Status

approved