A079229 - OEIS

%I #14 Aug 02 2013 10:48:53

%S 1,1,2,1,1,1,3,1,1,1,2,1,1,1,2,1,2,1,2,1,1,1,3,2,1,3,1,1,1,1,2,1,1,1,

%T 2,1,1,1,2,1,1,1,3,2,1,1,4,1,1,1,2,1,2,1,2,1,1,1,2,1,1,3,2,1,1,1,2,1,

%U 1,1,2,1,1,3,1,1,1,1,3,2,1,1,2,1,1,1,2,1,2,1,2,1,1,1,2,1,4,1,2,1,1,1,2,1,1

%N Least k>0 such that rad(n+k) > rad(n), where rad is the squarefree kernel (A007947).

%C A020754 probably gives the records in this sequence. - _Charles R Greathouse IV_, Aug 02 2013

%H Reinhard Zumkeller, <a href="/A079229/b079229.txt">Table of n, a(n) for n = 1..10000</a>

%t rad[n_] := Times @@ FactorInteger[n][[All, 1]]; a[1] = 1; a[n_] := For[k = 1, True, k++, If[ rad[n+k] > rad[n], Return[k]]]; Table[ a[n], {n, 1, 105}] (* _Jean-François Alcover_, Oct 05 2012 *)

%o (Haskell)

%o a079229 n = a079229_list !! (n-1)

%o a079229_list = f a007947_list where

%o    f (x:xs) = ((+ 1) . length $ takeWhile (<= x) xs) : f xs

%o -- _Reinhard Zumkeller_, Oct 06 2012

%o (PARI) rad(n)=my(f=factor(n)[,1]);prod(i=1,#f,f[i])

%o a(n)=my(r=rad(n),k);while(r>=rad(n+k++),);k \\ _Charles R Greathouse IV_, Aug 02 2013

%Y a(n) = A079228(n) - n.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Jan 02 2003