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
Keywords
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
Programs
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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
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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
Comments