A070323 - OEIS

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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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..26.

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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A001223, A037169, A081411.

Sequence in context: A096096 A300759 A100799 * A109213 A109214 A000301

Adjacent sequences: A070320 A070321 A070322 * A070324 A070325 A070326

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 11 2002

STATUS

approved