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A057475 Number of k, 1 <= k <= n, such that gcd(n,k) = gcd(n+1,k) = 1. 8
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; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Number of numbers between 1 and n-1 coprime to n(n+1).

It is conjectured that every positive integer appears. - Jon Perry, Dec 12 2002

LINKS

Table of n, a(n) for n=1..80.

FORMULA

From Reinhard Zumkeller, May 02 2006: (Start)

a(A000040(n)-1) = A000010(A000040(n)-1);

a(A000040(n)) = A000010(A000040(n)+1)-1;

a(A118854(n)-1) = a(A118854(n)). (End)

EXAMPLE

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

MATHEMATICA

f[ n_ ] := Length @ Select[ Range[ n ], GCD[ n, # ] == GCD[ n + 1, # ] == 1 & ]; Table[ f[ n ], {n, 80} ] (* Ray Chandler, Dec 06 2006 *)

PROG

(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)", "))

(MAGMA) [#[k:k in [1..n]| Gcd(n, k) eq Gcd(n+1, k) and Gcd(n, k) eq 1]: n in [1..80]]; // Marius A. Burtea, Oct 15 2019

CROSSREFS

Cf. A124738, A124739, A124740, A124741.

Sequence in context: A108617 A092683 A172089 * A024376 A230128 A123265

Adjacent sequences:  A057472 A057473 A057474 * A057476 A057477 A057478

KEYWORD

nonn

AUTHOR

Leroy Quet, Sep 27 2000

STATUS

approved

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Last modified April 8 02:27 EDT 2020. Contains 333312 sequences. (Running on oeis4.)