A362072 -id:A362072 - cp's OEIS frontend

A362073 a(n) is the permanent of the n X n symmetric matrix M(n) whose generic element M[i,j] = digsum(i*j).

1, 1, 8, 216, 7344, 168183, 7226091, 506792295, 43261224876, 5520748306176, 170835815638728, 19632554202684096, 2228687316428293152, 347514692118635694888, 62201193604462666921968, 8113764691750577654439864, 1557556394182730485102253088, 348394812690307787609428395792

Offset: 0

Stefano Spezia, Apr 08 2023

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

			a(6) = 7226091:
    [1, 2, 3, 4, 5, 6]
    [2, 4, 6, 8, 1, 3]
    [3, 6, 9, 3, 6, 9]
    [4, 8, 3, 7, 2, 6]
    [5, 1, 6, 2, 7, 3]
    [6, 3, 9, 6, 3, 9]

Cf. A003991, A007953, A336225, A353933, A362072, A362074 (rank).

M[i_, j_]:=Total[IntegerDigits[i*j]]; Join[{1}, Table[Permanent[Table[M[i, j], {i,  n}, {j, n}]], {n, 18}]]

a(n) = matpermanent(matrix(n, n, i, j, sumdigits(i*j))); \\ Michel Marcus, Apr 08 2023

Sum_{i=1..n} M[n-i+1,i] = A362072(n).

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

Original entry on oeis.org

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

Stefano Spezia, Apr 08 2023

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.

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

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

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

cp's OEIS Frontend

A362073 a(n) is the permanent of the n X n symmetric matrix M(n) whose generic element M[i,j] = digsum(i*j).

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