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A175836 a(n) = Product_{i=1..n} psi(i) where psi is the Dedekind psi function (A001615). 10
1, 3, 12, 72, 432, 5184, 41472, 497664, 5971968, 107495424, 1289945088, 30958682112, 433421549568, 10402117189632, 249650812551168, 5991619501228032, 107849151022104576, 3882569436795764736 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..423

Antal Bege, Hadamard product of GCD matrices, Acta Univ. Sapientiae, Mathematica, 1, 1 (2009) 43-49

Index to divisibility sequences

FORMULA

a(n) = A059381(n)/A001088(n).

MAPLE

A175836 := proc(n) option remember; local p; `if`(n<2, 1, n*mul(1+1/p, p=factorset(n))*A175836(n-1)) end: # Peter Luschny, Feb 28 2014

MATHEMATICA

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]

PROG

(PARI) a=direuler(p=2, 100, (1+X)/(1-p*X)); for(i=2, #a, a[i]*=a[i-1]); a

\\ Charles R Greathouse IV, Jul 29 2011

(Haskell)

a175836 n = a175836_list !! (n-1)

a175836_list = scanl1 (*) a001615_list

-- Reinhard Zumkeller, Mar 01 2014

CROSSREFS

Cf. A001615, A001088, A059381, A059382, A059383, A059384, A238498.

Sequence in context: A103366 A277457 A228386 * A020530 A147998 A052676

Adjacent sequences:  A175833 A175834 A175835 * A175837 A175838 A175839

KEYWORD

nonn

AUTHOR

Enrique Pérez Herrero, Sep 18 2010

STATUS

approved

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Last modified June 25 00:41 EDT 2017. Contains 288708 sequences.