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Number of numbers between 1 and n-1 that are coprime to n(n+1)(n+2).

0

`%I #13 May 07 2016 11:02:06
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`%S 0,1,1,1,1,2,2,2,2,2,3,3,2,3,4,5,5,5,4,4,5,6,6,6,6,7,8,6,7,8,9,9,6,7,
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`%T 8,11,10,8,9,9,11,11,10,10,11,14,13,12,11,12,15,16,13,12,11,14,17,14,
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`%U 15,15,16,17,14,15,15,19,20,14,15,16,23,23,18,18
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`%N Number of numbers between 1 and n-1 that are coprime to n(n+1)(n+2).
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`%C Does every integer appear?
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`%e a(10) is the number of numbers between 1 and 9 that are coprime to 10*11*12, which leaves 1 and 7, hence a(10) = 2.
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`%t Table[Count[Range[1,n-1],_?(CoprimeQ[#,(n(n+1)(n+2))]&)],{n,80}] (* _Harvey P. Dale_, May 07 2016 *)
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`%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(3); for (i=1,50,v[1]=i; v[2]=i+1; v[3]=i+2; print1(newphi(v)","))
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`%o (PARI) a(n) = sum(i=1, n-1, gcd(i, n*(n+1)*(n+2)) == 1); \\ _Michel Marcus_, Mar 17 2014
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`%K nonn
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`%O 1,6
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`%A _Jon Perry_, Dec 12 2002
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`%E More terms from _Michel Marcus_, Mar 17 2014
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