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A067393 Number of nonprimes among the numbers in {1,2,3,...,n!} which are relatively prime to n!. 0
1, 1, 1, 1, 1, 5, 67, 481, 4989, 51979, 570755, 5865449, 74226518, 904772855, 13111019601, 202135743076, 3307158697867, 53256981940267, 974755766640247, 17629139875485487, 357191085875727470, 7585952737111971220, 168542590546266903340, 3718034609300727209976 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..23.

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. A000142, A000720, A003604, A000010, A048855.

Sequence in context: A142009 A226412 A226343 * A212731 A316146 A113265

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

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Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)