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Let M_n be the n X n matrix m(i,j) = min(prime(i), prime(j)); then a(n) = det(M_n).
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%I #20 Aug 17 2022 22:41:47

%S 2,2,4,8,32,64,256,512,2048,12288,24576,147456,589824,1179648,4718592,

%T 28311552,169869312,339738624,2038431744,8153726976,16307453952,

%U 97844723712,391378894848,2348273369088,18786186952704,75144747810816

%N Let M_n be the n X n matrix m(i,j) = min(prime(i), prime(j)); then a(n) = det(M_n).

%C If A_n is the n X n matrix a(i,j) = Max(prime(i), prime(j)) then det(A_n)/det(M_n) = prime(n)/2.

%F a(n) = 2*A037169(n)/prime(n) for n > 1.

%F a(n) = 2*Product_{i=1..n-1} A001223(i) for n > 1. - _Luca Onnis_, Aug 13 2022

%F a(n) = 2 * A081411(n-1) for n >= 2. - _Alois P. Heinz_, Aug 17 2022

%t a[n_] := 2*Product[Differences[Prime[Range[100]]][[i]], {i, 1, n - 1}] *_Luca Onnis_, Aug 13 2022*

%o (PARI) a(n) = matdet(matrix(n, n, i, j, min(prime(i), prime(j)))); \\ _Michel Marcus_, Aug 13 2022

%Y Cf. A001223, A037169, A081411.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, May 11 2002