A078640 Number of numbers between 1 and n-1 that are coprime to n(n+1)(n+2).

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, 8, 11, 10, 8, 9, 9, 11, 11, 10, 10, 11, 14, 13, 12, 11, 12, 15, 16, 13, 12, 11, 14, 17, 14, 15, 15, 16, 17, 14, 15, 15, 19, 20, 14, 15, 16, 23, 23, 18, 18

Offset

1,6

Comments

Does every integer appear?

Links

Table of n, a(n) for n=1..74.

Example

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.

Mathematica

Table[Count[Range[1, n-1], _?(CoprimeQ[#, (n(n+1)(n+2))]&)], {n, 80}] (* Harvey P. Dale, May 07 2016 *)

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(3); for (i=1, 50, v[1]=i; v[2]=i+1; v[3]=i+2; print1(newphi(v)", "))
(PARI) a(n) = sum(i=1, n-1, gcd(i, n*(n+1)*(n+2)) == 1); \\ Michel Marcus, Mar 17 2014

Crossrefs

Sequence in context: A067752 A229942 A025422 * A006374 A193677 A281855

Adjacent sequences: A078637 A078638 A078639 * A078641 A078642 A078643

Keyword

nonn

Author

Jon Perry, Dec 12 2002

Extensions

More terms from Michel Marcus, Mar 17 2014

Status

approved