A202298 If A is the n X n matrix containing the first n^2 primes, a(n) is the sum of the elements of the square of A.

4, 155, 3702, 39933, 244676, 1046455, 3635046, 10406049, 26595892, 60712839, 128248632, 253217949, 472633812, 837636667, 1431878468, 2356057659, 3756191658, 5844567389, 8865989698, 13147819241, 19100995732, 27324708263, 38402817766, 53116446341, 72537301810, 97894517685

Offset: 1

Author

Stephen Balaban, Dec 15 2011

Keywords

• nonn

Examples

			M2 = [2,3; 5,7], M2*M2 = [19,27; 45,64], so a(2) = 19 + 27 + 45 + 64 = 155.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A109724.

Programs

Maple

A202298 := proc(n)
    local A,A2,r,c ;
    A := Matrix(n, n) ;
    for r from 0 to n-1 do
    for c from 0 to n-1 do
        A[r+1,c+1] := ithprime(1+r*n+c) ;
    end do:
    end do:
    A2 := A^2 ;
    add(add(A2[r,c],r=1..n),c=1..n) ;
end proc: # R. J. Mathar, Feb 09 2017
# alternative
N:= 50: # for a(1)..a(N)
P:= [seq(ithprime(i),i=1..N^2)]:
f:= proc(n) local M,e,u; M:= Matrix(n,n,P[1..n^2]);
   e:= Vector(n,1);
   e^%T . (M . (M . e));
end proc:
map(f, [$1..N]); # Robert Israel, Jan 11 2024

PARI

a(n) = my(m = matrix(n,n, i, j, prime((i-1)*n+j))); my(mm = m^2); sum(k=1, n, vecsum(mm[k,])); \\ Michel Marcus, Jan 28 2017

Formula

a(n) = Sum_{j=1..n} (Sum_{i=1..n} prime(i+n*(j-1)) * Sum_{i=1..n} prime(j+n*(i-1))). - Robert Israel, Jan 11 2024

Extensions

More terms from Michel Marcus, Jan 28 2017