A070323 Let M_n be the n X n matrix m(i,j) = min(prime(i), prime(j)); then a(n) = det(M_n).

2, 2, 4, 8, 32, 64, 256, 512, 2048, 12288, 24576, 147456, 589824, 1179648, 4718592, 28311552, 169869312, 339738624, 2038431744, 8153726976, 16307453952, 97844723712, 391378894848, 2348273369088, 18786186952704, 75144747810816

Offset: 1

Author

Benoit Cloitre, May 11 2002

Keywords

• easy
• nonn

Comments

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.

Crossrefs

Cf. A001223, A037169, A081411.

Programs

Mathematica

a[n_] := 2*Product[Differences[Prime[Range[100]]][[i]], {i, 1, n - 1}]; Table[a[n], {n, 1, 30}] (* Luca Onnis, Aug 13 2022 *)

PARI

a(n) = matdet(matrix(n, n, i, j, min(prime(i), prime(j)))); \\ Michel Marcus, Aug 13 2022

Formula

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

a(n) = 2*Product_{i=1..n-1} A001223(i) for n > 1. - Luca Onnis, Aug 13 2022

a(n) = 2 * A081411(n-1) for n >= 2. - Alois P. Heinz, Aug 17 2022