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Revision History for A073484

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A073484

Number of gaps in factors of the n-th squarefree number.
(history; published version)

#11 by Michel Marcus at Sat Apr 10 05:53:33 EDT 2021

STATUS

reviewed

approved

#10 by Joerg Arndt at Sat Apr 10 04:13:31 EDT 2021

STATUS

proposed

reviewed

#9 by Michel Marcus at Sat Apr 10 03:23:58 EDT 2021

STATUS

editing

proposed

Discussion

Sat Apr 10

03:39

Amiram Eldar: Yes.

#8 by Michel Marcus at Sat Apr 10 03:23:52 EDT 2021

FORMULA

a(A000040(n))=0; a(A006094(n))=0; a(A002110(n))=0; a(A073485(n))=0; a(A073486(n))>0; a(A073487(n))=1; a(A073488(n))=2; a(A073489(n))=3.

a(A073486(n))>0; a(A073487(n))=1; a(A073488(n))=2; a(A073489(n))=3.

STATUS

proposed

editing

Discussion

Sat Apr 10

03:23

Michel Marcus: ok ?

#7 by Amiram Eldar at Sat Apr 10 03:13:59 EDT 2021

STATUS

editing

proposed

#6 by Amiram Eldar at Sat Apr 10 02:58:55 EDT 2021

COMMENTS

a(A000040(n))=0; a(A006094(n))=0; a(A002110(n))=0; a(A073485(n))=0; a(A073486(n))>0; a(A073487(n))=1; a(A073488(n))=2; a(A073489(n))=3;

a(n)=0 iff A073483(n)=1.

FORMULA

a(A000040(n))=0; a(A006094(n))=0; a(A002110(n))=0; a(A073485(n))=0; a(A073486(n))>0; a(A073487(n))=1; a(A073488(n))=2; a(A073489(n))=3.

a(n)=0 iff A073483(n)=1.

#5 by Amiram Eldar at Sat Apr 10 02:58:14 EDT 2021

LINKS

Amiram Eldar, <a href="/A073484/b073484.txt">Table of n, a(n) for n = 1..10000</a>

MATHEMATICA

gaps[n_] := SequenceCount[FactorInteger[n][[;; , 1]], {p1_, p2_} /; p2 != NextPrime[p1], Overlaps -> True]; gaps /@ Select[Range[200], SquareFreeQ] (* Amiram Eldar, Apr 10 2021 *)

STATUS

approved

editing

#4 by Russ Cox at Fri Mar 30 18:50:25 EDT 2012

AUTHOR

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Aug 03 2002

Discussion

Fri Mar 30

18:50

OEIS Server: https://oeis.org/edit/global/246

#3 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Number of gaps in factors of the n-th square-free squarefree number.

EXAMPLE

The 69th square-free squarefree number is 110=2*5*11, therefore a(69)=2, as there are two gaps: between 2 and 5 and between 5 and 11.

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,new

nonn

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystemsgmail.com), Aug 03 2002