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A048855 Number of integers up to n! relatively prime to n!. 16
1, 1, 1, 2, 8, 32, 192, 1152, 9216, 82944, 829440, 8294400, 99532800, 1194393600, 16721510400, 250822656000, 4013162496000, 64210599936000, 1155790798848000, 20804234379264000, 416084687585280000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Rephrasing the Quet formula: Begin with 1. Then, if n + 1 is prime subtract 1 and multiply. If n+1 is not prime, multiply. Continue writing each product. Thus the sequence would begin 1, 2, 8, . . . . The first product is 1*(2 - 1), second is 1*(3 - 1), and third is 2*4. - Enoch Haga, May 06 2009

REFERENCES

Ronald L. Graham, D. E. Knuth and Oren Patashnik, "Concrete Mathematics, A Foundation for Computer Science," Addison-Wesley Publ. Co., Reading, MA, 1989, page 134.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..450

FORMULA

a(n) = phi(n!) = A000010(n!).

If n is composite, then a(n) = a(n-1)*n. If n is prime, then a(n) = a(n-1)*(n-1). - Leroy Quet, May 24 2007

Under the Riemann Hypothesis, a(n) = n! / (e^gamma * log n) * (1 + O(log n/sqrt(n))). - Charles R Greathouse IV, May 12 2011

MAPLE

with(numtheory):a:=n->phi(n!): seq(a(n), n=0..20); # Zerinvary Lajos, Oct 07 2007

MATHEMATICA

Table[ EulerPhi[ n! ], {n, 0, 21}] (* Robert G. Wilson v, Nov 21 2003 *)

PROG

(Sage) [euler_phi(factorial(n)) for n in xrange(0, 21)] # Zerinvary Lajos, Jun 06 2009

(PARI) a(n)=eulerphi(n!) \\ Charles R Greathouse IV, May 12 2011

CROSSREFS

Cf. A000142, A014197.

Sequence in context: A141202 A081358 A206303 * A262480 A062797 A134751

Adjacent sequences:  A048852 A048853 A048854 * A048856 A048857 A048858

KEYWORD

easy,nonn

AUTHOR

Paul Max Payton

EXTENSIONS

Name changed by Daniel Forgues, Aug 01 2011

STATUS

approved

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Last modified March 26 23:19 EDT 2017. Contains 284141 sequences.