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%I #24 Apr 19 2024 08:06:42
%S 1,2,12,144,4320,233280,29393280,7054387200,3555411148800,
%T 3519857037312000,7201627498340352000,28950542543328215040000,
%U 237104943429858081177600000,3853903750508913251460710400000,126138269754156730720309051392000000,8234306249551351381421774874869760000000,1079270520128695625562952032849179443200000000,282311265573183686952254740944556962034483200000000
%N Determinant of the n X n matrix m_(i,j) = gcd(2^i-1, 2^j-1).
%F a(n+1)/a(n) = A027375(n+1).
%F a(n) = (1/2)*Product_{k=1..n} Sum_{d|k} moebius(d)*2^(k/d).
%F a(n) ~ c * 2^(n*(n+1)/2), where c = 0.09412540696949274854160062245002977344042957885767746756023904566838799439... - _Vaclav Kotesovec_, Apr 19 2024
%t b[n_] := DivisorSum[n, MoebiusMu[n/#]*2^#& ]; a[n_] := a[n] = If[n == 1, 1, a[n-1]*b[n]]; Array[a, 18] (* _Jean-François Alcover_, Dec 18 2015 *)
%t Table[Det[Table[GCD[2^i-1,2^j-1],{i,n},{j,n}]],{n,20}] (* _Harvey P. Dale_, Sep 23 2022 *)
%o (PARI) a(n)=if(n<1,0,(1/2)*prod(k=1,n,sumdiv(k,d,moebius(d)*2^(k/d))))
%Y Cf. A001088, A027375.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Jan 03 2013
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