A055679 Number of distinct prime factors of phi(n!).

0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14

Offset

1,6

Comments

Number of distinct prime factors of n! and phi(n!) are respectively pi(n) and pi(floor(n/2)).

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

a(n) = A001221(A000010(A000142(n))) = A001221(A048855(n)).

a(n) = pi(floor(n/2)).

Mathematica

PrimeNu[EulerPhi[Range[90]!]] (* Harvey P. Dale, Sep 27 2011 *)

Prog

(PARI) for(n=1, 50, print1(omega(eulerphi(n!)), ", ")) \\ G. C. Greubel, May 19 2017
(PARI) a(n) = primepi(n\2); \\ Michel Marcus, Aug 13 2024

Crossrefs

Cf. A000010, A000142, A000720, A001221, A055718.

Sequence in context: A261104 A326032 A169990 * A056172 A285881 A091373

Adjacent sequences: A055676 A055677 A055678 * A055680 A055681 A055682

Keyword

nonn,easy

Author

Labos Elemer, Jul 11 2000

Status

approved