A175836 a(n) = Product_{i=1..n} psi(i) where psi is the Dedekind psi function (A001615).

1, 3, 12, 72, 432, 5184, 41472, 497664, 5971968, 107495424, 1289945088, 30958682112, 433421549568, 10402117189632, 249650812551168, 5991619501228032, 107849151022104576, 3882569436795764736

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

Eric Weisstein's World of Mathematics, Le Paige's Theorem

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.

Cf. A239672.

Sequence in context: A277457 A367117 A228386 * A293138 A319948 A020530

Adjacent sequences: A175833 A175834 A175835 * A175837 A175838 A175839

Keyword

nonn

Author

Enrique Pérez Herrero, Sep 18 2010

Status

approved