A075426 Smallest initial value k that reaches 1 in n steps when iterating the map m -> rad(m)-1, where rad(m) is the squarefree kernel of m (A007947).

1, 2, 3, 6, 7, 14, 15, 30, 31, 62, 95, 318, 319, 734, 959, 2798, 2879, 5758, 5759, 11518, 11519, 23038, 23039, 46078, 46079, 92158, 92159, 184318, 184319, 368638, 368639, 737278, 737279, 1548286, 1548287, 3096574, 5160959, 10321918, 10321919

Offset: 0

Author

Reinhard Zumkeller, Sep 15 2002

Keywords

• nonn

Comments

Least k such that A075425(k) = n;

Observations: a(n) = n mod 2; frequently a(2k)+1 = a(2k+1) and a(2k) = 2*a(2k-1). a(n)=A075427(n-1) for n<=9.

Also A110157(a(n)) = n and A110157(m) < n for m < a(n).

Links

• Charles R Greathouse IV and Donovan Johnson, Table of n, a(n) for n = 0..56 (terms up to a(50) from Charles R Greathouse IV)

Programs

Haskell

import Data.List (elemIndex); import Data.Maybe (fromJust)
a075426 = (+ 1) . fromJust . (`elemIndex` a075425_list)
-- Reinhard Zumkeller, Aug 14 2013

PARI

rad(n)=my(f=factor(n)[, 1]); prod(i=1, #f, f[i])
A075425(n)=if(n<4, n, 1+A075425(rad(n)-1))
r=0;for(n=1,1e8,t=A075425(n);if(t>r,r=t;print1(n", "))) \\ Charles R Greathouse IV, Aug 08 2013

Extensions

a(33)-a(38) from Donovan Johnson, Aug 27 2010