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

0,6

Links

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

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A142009 A226412 A226343 * A212731 A316146 A380403

Adjacent sequences: A067390 A067391 A067392 * A067394 A067395 A067396

Keyword

nonn

Author

Labos Elemer, Jan 22 2002

Extensions

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

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

Status

approved