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Search: id:A001783
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| A001783 |
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n-phi-torial, or phi-torial of n: Product k, 1<=k<=n, k relatively prime to n.
(Formerly M0921 N0346)
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+0
8
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| 1, 1, 2, 3, 24, 5, 720, 105, 2240, 189, 3628800, 385, 479001600, 19305, 896896, 2027025, 20922789888000, 85085, 6402373705728000, 8729721, 47297536000, 1249937325, 1124000727777607680000, 37182145, 41363226782215962624
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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In other words, a(1) = 1, and for n >= 2, a(n) = product of the phi(n) numbers < n and relatively prime to n.
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REFERENCES
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Problem E1045, Amer. Math. Monthly, 60 (1953), 422.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
Eric Weisstein's World of Mathematics, Wilson's Theorem
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FORMULA
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a(n)=n^phi(n)*Product_{d|n} (d!/d^d)^mu(n/d); phi=A000010 is the Euler totient function and mu=A008683 the Moebius function (Tom M. Apostol, Introduction to Analytic Number Theory, New York 1984, p. 48). - Franz Vrabec (franz.vrabec(AT)planetuniqa.at), Jul 08 2005
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MAPLE
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A001783 := proc(n) local i, t1; t1 := 1; for i from 1 to n do if gcd(i, n)=1 then t1 := t1*i; fi; od; t1; end;
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CROSSREFS
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Cf. A023896, A066570.
Sequence in context: A115031 A030418 A037277 this_sequence A095996 A061098 A119619
Adjacent sequences: A001780 A001781 A001782 this_sequence A001784 A001785 A001786
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999
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