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A067549 Determinant of n X n matrix whose diagonal are the first n primes and all other elements are 1's.

%I A067549 #12 Feb 21 2018 04:43:05
%S A067549 2,5,22,140,1448,17856,291456,5338368,119102976,3371378688,
%T A067549 102163230720,3708532408320,149444916019200,6320831260262400,
%U A067549 292612319045222400,15301128319716556800,891900404470539878400,53771252059997208576000,3564336303465704718336000
%N A067549 Determinant of n X n matrix whose diagonal are the first n primes and all other elements are 1's.
%H A067549 Iain Fox, <a href="/A067549/b067549.txt">Table of n, a(n) for n = 1..300</a>
%e A067549 The matrix begins:
%e A067549   2  1  1  1  1  1  1 ...
%e A067549   1  3  1  1  1  1  1 ...
%e A067549   1  1  5  1  1  1  1 ...
%e A067549   1  1  1  7  1  1  1 ...
%e A067549   1  1  1  1 11  1  1 ...
%e A067549   1  1  1  1  1 13  1 ...
%p A067549 d:=(i,j)->`if`(i<>j,1,ithprime(i)):
%p A067549 seq(LinearAlgebra[Determinant](Matrix(n,d)),n=1..20); # _Muniru A Asiru_, Feb 16 2018
%t A067549 Table[ Det[ DiagonalMatrix[ Table[ Prime[ i ] - 1, {i, 1, n} ] ] + 1 ], {n, 1, 20} ]
%o A067549 (PARI) a(n) = matdet(matrix(n, n, i, j, if(i == j, prime(i), 1))) \\ _Iain Fox_, Feb 15 2018
%K A067549 nonn
%O A067549 1,1
%A A067549 _Robert G. Wilson v_, Jan 28 2002
%E A067549 a(18)-a(19) from _Iain Fox_, Feb 15 2018