

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
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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," AddisonWesley 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(n1)*n. If n is prime, then a(n) = a(n1)*(n1).  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



