OFFSET
1,1
COMMENTS
The values 1, 2 and 3 occur 309008, 251134 and 439858 times, respectively, in the first 1000000 terms. - Rick L. Shepherd, Jul 25 2006
From Reinhard Zumkeller, Jan 20 2008: (Start)
1 <= a(n) <= 3.
(End)
Also the lengths of runs in A243348, differences of the n-th squarefree number and n. - Antti Karttunen, Jun 06 2014
LINKS
A. Karttunen & R. Zumkeller (the first 1000 terms), Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Squarefree
EXAMPLE
The runs of squarefree integers are as follows: (1,2,3), (5,6,7), (10,11), (13,14,15), (17), (19), (21,22,23),...
MAPLE
with(numtheory): a:=proc(n) if mobius(n)=0 then n else fi end: A:=[0, seq(a(n), n=1..500)]: b:=proc(n) if A[n]-A[n-1]>1 then A[n]-A[n-1]-1 else fi end: seq(b(n), n=2..nops(A)); # Emeric Deutsch, Jul 24 2006
MATHEMATICA
t = {}; cnt = 0; Do[If[SquareFreeQ[n], cnt++, If[cnt > 0, AppendTo[t, cnt]; cnt = 0]], {n, 500}]; t (* T. D. Noe, Mar 19 2013 *)
PROG
(PARI) n=1; while(n<1000, c=0; while(issquarefree(n), n++; c++); print1(c, ", "); while(!issquarefree(n), n++)) \\ Rick L. Shepherd, Jul 25 2006
(Scheme, with Antti Karttunen's IntSeq-library)
(define (A120992 n) (if (= n 1) (Aincr_points_of_A243348 n) (- (Aincr_points_of_A243348 n) (Aincr_points_of_A243348 (- n 1)))))
;; Using these two auxiliary functions, not submitted separately:
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Jul 21 2006
EXTENSIONS
More terms from Emeric Deutsch and Rick L. Shepherd, Jul 25 2006
STATUS
approved