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Search: id:A048855
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| A048855 |
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Number of integers less than n! relatively prime to n!. |
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+0
14
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| 1, 1, 1, 2, 8, 32, 192, 1152, 9216, 82944, 829440, 8294400, 99532800, 1194393600, 16721510400, 250822656000, 4013162496000, 64210599936000, 1155790798848000, 20804234379264000, 416084687585280000
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Contribution from Enoch Haga (Enokh(AT)comcast.net), May 06 2009: (Start)
Another way to explain the sequence is to 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. (End)
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REFERENCES
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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.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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Euler phi(n!).
Phi(n) = n * Product for all primes which divide n, (1 - 1/p).
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
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MAPLE
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with(numtheory):a:=n->phi(n!): seq(a(n), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007
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MATHEMATICA
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Table[ EulerPhi[ n! ], {n, 0, 21}] (from Robert G. Wilson v Nov 21 2003)
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PROGRAM
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(Other) sage: [euler_phi(factorial(n))for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2009]
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CROSSREFS
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Cf. A000142, A014197.
Sequence in context: A009753 A141202 A081358 this_sequence A062797 A134751 A139014
Adjacent sequences: A048852 A048853 A048854 this_sequence A048856 A048857 A048858
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KEYWORD
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easy,nonn
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AUTHOR
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Paul M. Payton (paul.payton(AT)lmco.com)
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