A067393 Number of nonprimes among the numbers in {1,2,3,...,n!} which are relatively prime to n!.

1, 1, 1, 1, 1, 5, 67, 481, 4989, 51979, 570755, 5865449, 74226518, 904772855, 13111019601, 202135743076, 3307158697867, 53256981940267, 974755766640247, 17629139875485487, 357191085875727470, 7585952737111971220, 168542590546266903340, 3718034609300727209976

Offset: 0

Author

Labos Elemer, Jan 22 2002

Keywords

• nonn

Examples

			For n = 5, n! = 120, a(5) = phi(120) - pi(120) + pi(5) = 32 - 30 + 3 = 5; the 5 nonprimes are 1, 49, 77, 91, 119.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..25 (calculated using the b-file at A003604)

Crossrefs

Cf. A000010, A000142, A000720, A003604, A048855.

Programs

Mathematica

a[n_] := EulerPhi[ n! ]-PrimePi[ n! ]+PrimePi[n]

Formula

a(n) = phi(n!) - pi(n!) + pi(n) = A000010(n!) - A000720(n!) + A000720(n).

Extensions

a(18)-a(19) from Donovan Johnson, Mar 24 2011

a(20)-a(23) from Giovanni Resta, Oct 29 2019