A075425 Number of steps to reach 1 starting with n and iterating the map n ->rad(n)-1, where rad(n) is the squarefree kernel of n (A007947).

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

Offset: 1

Author

Reinhard Zumkeller, Sep 15 2002

Keywords

• nonn

Comments

Sequence is defined for all n, as A075423(n) < n.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Haskell

a075425 n = snd $ until ((== 1) . fst)
                        (\(x, i) -> (a075423 x, i + 1)) (n, 0)
-- Reinhard Zumkeller, Aug 14 2013

PARI

rad(n)=vecprod(factor(n)[,1])
a(n)=my(k);while(n>1,n=rad(n)-1;k++); k \\ Charles R Greathouse IV, Jul 09 2013