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A175836
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a(n) = Product_{i=1..n} psi(i) where psi is the Dedekind psi function (A001615).
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10
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1, 3, 12, 72, 432, 5184, 41472, 497664, 5971968, 107495424, 1289945088, 30958682112, 433421549568, 10402117189632, 249650812551168, 5991619501228032, 107849151022104576, 3882569436795764736
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OFFSET
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1,2
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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) = A060648(gcd(i,j)) for 1 <= i,j <= n, note that A060648 is the Inverse Möbius transform of A001615. - Enrique Pérez Herrero, Aug 12 2011
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LINKS
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FORMULA
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MAPLE
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MATHEMATICA
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JordanTotient[n_, k_:1]:=DivisorSum[n, #^k*MoebiusMu[n/# ]&]/; (n>0)&&IntegerQ[n];
DedekindPsi[n_]:=JordanTotient[n, 2]/EulerPhi[n];
A175836[n_]:=Times@@DedekindPsi/@Range[n]
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PROG
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(PARI) a=direuler(p=2, 100, (1+X)/(1-p*X)); for(i=2, #a, a[i]*=a[i-1]); a
(Haskell)
a175836 n = a175836_list !! (n-1)
a175836_list = scanl1 (*) a001615_list
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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