A362074 a(n) is the rank of the n X n symmetric matrix M(n) whose generic element M[i,j] = digsum(i*j).

1, 1, 1, 3, 5, 6, 7, 7, 7, 7, 7, 9, 11, 11, 13, 14, 15, 16, 18, 18, 18, 19, 19, 21, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63

Offset

1,4

Comments

The matrix M(n) is nonsingular (a(n) = n) only for n = 1, 5, 6 and 7 with determinant equal respectively to 1, 6561, 59049 and -531441.

Links

Table of n, a(n) for n=1..69.

Mathematica

M[i_, j_]:=Total[IntegerDigits[i*j]]; Table[MatrixRank[Table[M[i, j], {i,  n}, {j, n}]], {n, 69}]

Prog

(PARI) a(n)=matrank(matrix(n, n, i, j, sumdigits(i*j))) \\ Andrew Howroyd, Apr 08 2023

Crossrefs

Cf. A003991, A007953, A353933, A362072, A362073 (permanent).

Sequence in context: A111612 A317920 A305443 * A122818 A070083 A316851

Adjacent sequences: A362071 A362072 A362073 * A362075 A362076 A362077

Keyword

nonn,base

Author

Stefano Spezia, Apr 08 2023

Status

approved