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A001088
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Product of totient function: a(n) = Product_{k=1..n} phi(k) (cf. A000010).
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33
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1, 1, 1, 2, 4, 16, 32, 192, 768, 4608, 18432, 184320, 737280, 8847360, 53084160, 424673280, 3397386240, 54358179840, 326149079040, 5870683422720, 46965467381760, 563585608581120, 5635856085811200, 123988833887846400, 991910671102771200, 19838213422055424000
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OFFSET
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0,4
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COMMENTS
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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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D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, p. 598.
M. Petkovsek et al., A=B, Peters, 1996, p. 21.
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LINKS
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FORMULA
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a(n) = phi(1) * phi(2) * ... * phi(n).
Limit_{n->infinity} a(n)^(1/n) / n = exp(-1) * A124175 = 0.205963050288186353879675428232497466485878059342058515016427881513657493... (see Mathoverflow link). - Vaclav Kotesovec, Jun 09 2021
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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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MATHEMATICA
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Rest[FoldList[Times, 1, EulerPhi[Range[30]]]] (* Harvey P. Dale, Dec 09 2011 *)
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PROG
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(Haskell)
a001088 n = a001088_list !! (n-1)
a001088_list = scanl1 (*) a000010_list
(GAP) List([1..30], n->Product([1..n], i->Phi(i))); # Muniru A Asiru, Jul 31 2018
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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