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

1,3

Links

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

Formula

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

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}]

Prog

(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

Crossrefs

Cf. A095996.

Sequence in context: A099735 A322352 A091279 * A082175 A129292 A126606

Adjacent sequences: A095999 A096000 A096001 * A096003 A096004 A096005

Keyword

nonn

Author

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

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

Status

approved