The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A120992

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A120992

Number of integers in n-th run of squarefree positive integers.
(history; published version)

#35 by N. J. A. Sloane at Fri Feb 28 12:06:08 EST 2025

STATUS

proposed

approved

#34 by Robert C. Lyons at Fri Feb 28 11:58:25 EST 2025

STATUS

editing

proposed

#33 by Robert C. Lyons at Fri Feb 28 11:58:21 EST 2025

PROG

(Scheme)

(Scheme, with _; ; With _Antti Karttunen_'s IntSeq-library).

STATUS

approved

editing

#32 by Charles R Greathouse IV at Sun Feb 16 08:33:02 EST 2025

LINKS

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/Squarefree.html">Squarefree</a>

Discussion

Sun Feb 16

08:33

OEIS Server: https://oeis.org/edit/global/3014

#31 by Peter Luschny at Sat Apr 13 07:08:56 EDT 2019

STATUS

reviewed

approved

#30 by Joerg Arndt at Sat Apr 13 04:55:12 EDT 2019

STATUS

proposed

reviewed

#29 by Michel Marcus at Sat Apr 13 04:17:31 EDT 2019

STATUS

editing

proposed

#28 by Michel Marcus at Sat Apr 13 04:17:16 EDT 2019

COMMENTS

A136742(n) = PRODUCTProduct{k=0..a(n)} (A072284(n)+k:0<=k<a(n)).

A136743(n) = SUMSum_{k=0..a(n)} A001221(A072284(n)+k):0<=k<a(n)).

(End)

From Antti Karttunen, Jun 06 2014: (Start)

Also the lengths of runs in A243348, differences of the n-th squarefree number and n.

Also the lengths of runs in A243348, differences of the n-th squarefree number and n. - Antti Karttunen, Jun 06 2014

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

STATUS

approved

editing

#27 by Jon E. Schoenfield at Tue Jul 07 22:31:06 EDT 2015

STATUS

editing

approved

#26 by Jon E. Schoenfield at Tue Jul 07 22:31:03 EDT 2015

COMMENTS

Also the lengths of runs in A243348, differences of the n-th square-free squarefree number and n.

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

STATUS

approved

editing