|
%I #45 Feb 03 2023 07:33:17
%S 1,3,12,72,432,5184,41472,497664,5971968,107495424,1289945088,
%T 30958682112,433421549568,10402117189632,249650812551168,
%U 5991619501228032,107849151022104576,3882569436795764736
%N a(n) = Product_{i=1..n} psi(i) where psi is the Dedekind psi function (A001615).
%C 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
%H Charles R Greathouse IV, <a href="/A175836/b175836.txt">Table of n, a(n) for n = 1..423</a>
%H Antal Bege, <a href="http://www.emis.de/journals/AUSM/C1-1/MATH1-4.PDF">Hadamard product of GCD matrices</a>, Acta Univ. Sapientiae, Mathematica, 1, 1 (2009) 43-49
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LePaigesTheorem.html">Le Paige's Theorem</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F a(n) = A059381(n)/A001088(n).
%p 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
%t JordanTotient[n_,k_:1]:=DivisorSum[n,#^k*MoebiusMu[n/# ]&]/;(n>0)&&IntegerQ[n];
%t DedekindPsi[n_]:=JordanTotient[n,2]/EulerPhi[n];
%t A175836[n_]:=Times@@DedekindPsi/@Range[n]
%o (PARI) a=direuler(p=2, 100, (1+X)/(1-p*X));for(i=2,#a,a[i]*=a[i-1]);a
%o \\ _Charles R Greathouse IV_, Jul 29 2011
%o (Haskell)
%o a175836 n = a175836_list !! (n-1)
%o a175836_list = scanl1 (*) a001615_list
%o -- _Reinhard Zumkeller_, Mar 01 2014
%Y Cf. A001615, A001088, A059381, A059382, A059383, A059384, A238498.
%Y Cf. A239672.
%K nonn
%O 1,2
%A _Enrique Pérez Herrero_, Sep 18 2010
| 