A067549 Determinant of n X n matrix whose diagonal are the first n primes and all other elements are 1's.
2, 5, 22, 140, 1448, 17856, 291456, 5338368, 119102976, 3371378688, 102163230720, 3708532408320, 149444916019200, 6320831260262400, 292612319045222400, 15301128319716556800, 891900404470539878400, 53771252059997208576000, 3564336303465704718336000
Offset: 1
Keywords
Examples
The matrix begins: 2 1 1 1 1 1 1 ... 1 3 1 1 1 1 1 ... 1 1 5 1 1 1 1 ... 1 1 1 7 1 1 1 ... 1 1 1 1 11 1 1 ... 1 1 1 1 1 13 1 ...
Links
- Iain Fox, Table of n, a(n) for n = 1..300
Programs
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Maple
d:=(i,j)->`if`(i<>j,1,ithprime(i)): seq(LinearAlgebra[Determinant](Matrix(n,d)),n=1..20); # Muniru A Asiru, Feb 16 2018
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Mathematica
Table[ Det[ DiagonalMatrix[ Table[ Prime[ i ] - 1, {i, 1, n} ] ] + 1 ], {n, 1, 20} ] -
PARI
a(n) = matdet(matrix(n, n, i, j, if(i == j, prime(i), 1))) \\ Iain Fox, Feb 15 2018
Extensions
a(18)-a(19) from Iain Fox, Feb 15 2018