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A120992 Number of integers in n-th run of squarefree positive integers. 8
3, 3, 2, 3, 1, 1, 3, 1, 3, 3, 3, 3, 2, 1, 1, 1, 3, 2, 3, 3, 2, 3, 2, 3, 1, 1, 3, 1, 3, 3, 3, 3, 2, 2, 1, 3, 2, 3, 3, 2, 1, 1, 2, 3, 1, 1, 3, 1, 2, 3, 3, 3, 2, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 1, 1, 3, 1, 2, 1, 1, 3, 3, 2, 3, 1, 1, 2, 2, 3, 3, 2, 1, 1, 2, 3, 1 (list; graph; refs; listen; history; text; internal format)
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.

A136742(n) = Product{k=0..a(n)} (A072284(n)+k).

A136743(n) = Sum_{k=0..a(n)} A001221(A072284(n)+k).

(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:

(define Aincr_points_of_A243348 (COMPOSE -1+ (NONZERO-POS 1 1 Afirst_diffs_of_A243348)))

(define (Afirst_diffs_of_A243348 n) (if (< n 2) (- n 1) (- (A243348 n) (A243348 (- n 1)))))

CROSSREFS

Cf. A005117, A076259, A013928, A013929, A053797, A053806, A120993, A243348.

Sequence in context: A292600 A014967 A210851 * A129979 A228483 A274709

Adjacent sequences:  A120989 A120990 A120991 * A120993 A120994 A120995

KEYWORD

nonn

AUTHOR

Leroy Quet, Jul 21 2006

EXTENSIONS

More terms from Emeric Deutsch and Rick L. Shepherd, Jul 25 2006

STATUS

approved

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Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)