A204118 Symmetric matrix based on f(i,j) = gcd(prime(i), prime(j)), by antidiagonals.

2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,1

Comments

A204118 represents the matrix M given by f(i,j) = gcd(prime(i), prime(j)) for i >= 1 and j >= 1. See A204119 for characteristic polynomials of principal submatrices of M, with interlacing zeros. See A204016 for a guide to other choices of M.

Links

Table of n, a(n) for n=1..98.

Example

Northwest corner:
  2  1  1  1  1
  1  3  1  1  1
  1  1  5  1  1
  1  1  1  7  1
  1  1  1  1 11

Mathematica

f[i_, j_] := GCD[Prime[i], Prime[j]];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8 X 8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 15}, {i, 1, n}]]  (* A204118 *)
p[n_] := CharacteristicPolynomial[m[n], x];
c[n_] := CoefficientList[p[n], x]
TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
Table[c[n], {n, 1, 12}]
Flatten[%]                 (* A204119 *)
TableForm[Table[c[n], {n, 1, 10}]]

Crossrefs

Cf. A204119, A204016, A202453.

Sequence in context: A104967 A098495 A175432 * A095025 A274382 A318997

Adjacent sequences: A204115 A204116 A204117 * A204119 A204120 A204121

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 11 2012

Status

approved