%I #17 Sep 07 2024 08:53:25
%S 1,1,1,1,1,5,67,481,4989,51979,570755,5865449,74226518,904772855,
%T 13111019601,202135743076,3307158697867,53256981940267,
%U 974755766640247,17629139875485487,357191085875727470,7585952737111971220,168542590546266903340,3718034609300727209976
%N Number of nonprimes among the numbers in {1,2,3,...,n!} which are relatively prime to n!.
%H Amiram Eldar, <a href="/A067393/b067393.txt">Table of n, a(n) for n = 0..25</a> (calculated using the b-file at A003604)
%F a(n) = phi(n!) - pi(n!) + pi(n) = A000010(n!) - A000720(n!) + A000720(n).
%e 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.
%t a[n_] := EulerPhi[ n! ]-PrimePi[ n! ]+PrimePi[n]
%Y Cf. A000010, A000142, A000720, A003604, A048855.
%K nonn
%O 0,6
%A _Labos Elemer_, Jan 22 2002
%E a(18)-a(19) from _Donovan Johnson_, Mar 24 2011
%E a(20)-a(23) from _Giovanni Resta_, Oct 29 2019