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%I #21 Sep 08 2022 08:45:02
%S 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,
%T 9,11,8,12,17,11,9,16,11,12,19,11,11,22,15,14,17,13,15,24,17,14,17,15,
%U 17,28,15,16,29,17,18,24,15,20,31,21,15,24,23,24,35,19,19,28,18,24,31,22
%N Number of k, 1 <= k <= n, such that gcd(n,k) = gcd(n+1,k) = 1.
%C Number of numbers between 1 and n-1 coprime to n(n+1).
%C It is conjectured that every positive integer appears. - _Jon Perry_, Dec 12 2002
%F From _Reinhard Zumkeller_, May 02 2006: (Start)
%F a(A000040(n)-1) = A000010(A000040(n)-1);
%F a(A000040(n)) = A000010(A000040(n)+1)-1;
%F a(A118854(n)-1) = a(A118854(n)). (End)
%e a(8) = 3 because 1, 5 and 7 are all relatively prime to both 8 and 9.
%e a(9) counts those numbers coprime to 90, i.e. 1 and 7, hence a(9)=2
%t f[ n_ ] := Length @ Select[ Range[ n ], GCD[ n, # ] == GCD[ n + 1, # ] == 1 & ]; Table[ f[ n ], {n, 80} ] (* _Ray Chandler_, Dec 06 2006 *)
%o (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)","))
%o (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
%Y Cf. A124738, A124739, A124740, A124741.
%K nonn
%O 1,4
%A _Leroy Quet_, Sep 27 2000
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