A298883 Determinant of n X n matrix whose elements are m(i,j) = prime(i)^j.

1, 2, 6, 180, 50400, 958003200, 131514679296000, 1352181326649753600000, 112703642894318944282214400000, 903025586371469323704949549301760000000, 2012769637740033870687308804001121075357286400000000

Offset: 0

Author

Andres Cicuttin, Jan 28 2018

Keywords

• nonn

Comments

Traces of these matrices are A087480.

Examples

			For n=1:
          |2| = 2, then a(1) = 2.
For n=2:
          |2  4| = 6, then a(2) = 6.
          |3  9|
For n=3:
          |2  4   8| = 180, then a(3) = 180.
          |3  9  27|
          |5 25 125|
		

Links

• Robert Israel, Table of n, a(n) for n = 0..35
• Wikipedia, Vandermonde matrix

Crossrefs

Cf. A080358, A087480, A298903.

Programs

Maple

with(LinearAlgebra):
a:= n-> Determinant(Matrix(n, (i,j)-> ithprime(i)^j)):
seq(a(n), n=0..12);  # Alois P. Heinz, Jan 28 2018
# Alternative:
f:= proc(n) local P;
P:= [seq(ithprime(i),i=1..n)];
convert(P,`*`)*mul(mul(P[j]-P[i],j=i+1..n),i=1..n-1)
end proc:
map(f, [$0..20]); # Robert Israel, Jan 29 2018

Mathematica

a[n_]:=Table[Prime[i]^j,{i,1,n},{j,1,n}];
Table[Det[a[n]],{n,1,10}]

PARI

a(n) = matdet(matrix(n, n, i, j, prime(i)^j)); \\ Michel Marcus, Jan 28 2018

Formula

a(n) = Product_{1<=i<=n} prime(i) * Product_{1<=iRobert Israel, Jan 29 2018