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Search: id:A001088
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| A001088 |
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phi(1)*phi(2)*...*phi(n). |
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+0
11
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| 1, 1, 2, 4, 16, 32, 192, 768, 4608, 18432, 184320, 737280, 8847360, 53084160, 424673280, 3397386240, 54358179840, 326149079040, 5870683422720, 46965467381760, 563585608581120, 5635856085811200, 123988833887846400
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) is also the determinant of the symmetric n X n matrix M defined by M(i,j) = gcd(i,j) for 1 <= i,j <= n [Smith and Mansion]. - Avi Peretz (njk(AT)netvision.net.il), Mar 20 2001
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REFERENCES
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E. C. Catalan, Theoreme de MM. Smith et Mansion, Nouvelle correspondance mathematique, 4 (1878) 103-112.
D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, p. 598.
Warren P. Johnson, An LDU Factorization in Elementary Number Theory, Mathematics Magazine, 76 (2003), 392-394.
M. Petkovsek et al., A=B, Peters, 1996, p. 21.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..100
Eric Weisstein's World of Mathematics, Le Paige's Theorem
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EXAMPLE
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a(2) = 1 because the matrix M is: [1,1; 1,2] and det(A) = 1
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MAPLE
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with(numtheory, phi); A001088 := proc(n) local i; mul(phi(i), i=1..n); end;
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CROSSREFS
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Cf. A000010, A060238, A060239.
Adjacent sequences: A001085 A001086 A001087 this_sequence A001089 A001090 A001091
Sequence in context: A081411 A094384 A053038 this_sequence A101926 A087965 A074411
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Simon Plouffe (plouffe(AT)math.uqam.ca)
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EXTENSIONS
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Catalan reference from DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 22 2003
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