A096002 Let {b(n)} = A095996; then a(n) = number of terms {b(1),b(2),...,b(n-1)} which are coprime to n.

0, 1, 2, 2, 4, 2, 6, 4, 4, 3, 10, 3, 12, 4, 3, 8, 16, 4, 18, 4, 4, 6, 22, 5, 8, 7, 10, 5, 28, 2, 30, 16, 5, 9, 5, 7, 36, 10, 6, 6, 40, 3, 42, 7, 5, 12, 46, 9, 12, 7, 7, 8, 52, 10, 6, 7, 8, 15, 58, 3, 60, 16, 6, 32, 6, 3, 66, 10, 9, 3, 70, 13, 72, 19, 7, 11, 7, 4, 78, 10

Offset: 1

Author

Robert G. Wilson v, Jul 19 2004, based on a suggestion from Leroy Quet, Jun 18 2004

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A095996.

Programs

Mathematica

f[n_] := f[n] = Select[Divisors[n! ], GCD[ #, n] == 1 &][[ -1]]; Table[ Length[ Select[ Range[n - 1], GCD[ f[ # ], n] == 1 &]], {n, 2, 33}]

PARI

seq(n)={my(v=vector(n, n, denominator(n^n/n!))); vector(n, n, sum(k=1, n-1, gcd(v[k],n)==1));} \\ Andrew Howroyd, Nov 05 2019

Formula

If p is prime, then a(p) = p-1.

Extensions

a(33) - a(41) from Robert G. Wilson v, May 05 2013

a(1) corrected and terms a(42) and beyond from Andrew Howroyd, Nov 05 2019