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Search: id:A057475
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| A057475 |
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Number of k, 1 <= k <= n, such that GCD(n,k) = GCD(n+1,k) = 1. |
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+0
8
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| 1, 1, 1, 2, 1, 2, 3, 3, 2, 4, 3, 4, 5, 3, 4, 8, 5, 6, 7, 5, 5, 10, 7, 7, 9, 8, 8, 12, 7, 8, 15, 10, 9, 11, 8, 12, 17, 11, 9, 16, 11, 12, 19, 11, 11, 22, 15, 14, 17, 13, 15, 24, 17, 14, 17, 15, 17, 28, 15, 16, 29, 17, 18, 24, 15, 20, 31, 21, 15, 24, 23, 24, 35, 19, 19, 28, 18, 24, 31, 22
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Number of numbers between 1 and n-1 coprime to n(n+1).
It is conjectured that every positive integer appears. - Jon Perry (perry(AT)globalnet.co.uk), Dec 12 2002
a(A000040(n)-1)=A000010(A000040(n)-1); a(A000040(n))=A000010(A000040(n)+1)-1; = a(A118854(n)-1)=a(A118854(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 02 2006
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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a(8) = 3 because 1, 5 and 7 are all relatively prime to both 8 and 9.
a(9) counts those numbers coprime to 90, i.e. 1 and 7, hence a(9)=2
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MATHEMATICA
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f[ n_ ] := Length @ Select[ Range[ n ], GCD[ n, # ] == GCD[ n + 1, # ] == 1 & ]; Table[ f[ n ], {n, 80} ] (*Chandler*)
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PROGRAM
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(PARI) newphi(v)=local(vl, fl, np); vl=length(v); np=0; for (s=1, v[1], fl=false; for (r=1, vl, if (gcd(s, v[r])>1, fl=true; break)); if (fl==false, np++)); np v=vector(2); for (i=1, 500, v[1]=i; v[2]=i+1; print1(newphi(v)", "))
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CROSSREFS
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Cf. A124738, A124739, A124740, A124741.
Sequence in context: A039913 A108617 A092683 this_sequence A024376 A123265 A104345
Adjacent sequences: A057472 A057473 A057474 this_sequence A057476 A057477 A057478
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Sep 27 2000
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