A069743 -id:A069743 - cp's OEIS frontend

A069742 Duplicate of A069743.

1, 1, 1, 169, 57122, 1130708969104, 60520841316555286464512

Offset: 1

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A379913 Let M_n be the n X n matrix M_(i,j)=1/(3^i+3^j), then a(n) is the denominator of det(M_n).

6, 432, 145800, 28934010000, 36195844320916875, 8087414520398390420149816875, 14739121497834560950873288612087606246265625, 24111787175394014554749263306909156210251310885835206605812890625, 30311902674167553291682092445492621447523310843996437232420613554400185533411542126171875

Offset: 1

Robert Israel, Jan 06 2025

nonn

			For n = 3, the determinant of the matrix [1/6, 1/12, 1/30; 1/12, 1/18, 1/36; 1/30, 1/36, 1/54] is 1/145800, so a(3) = 145800.

Robert Israel, Table of n, a(n) for n = 1..20

Numerators are A069743.

g:= proc(n) local M;
  M:= Matrix(n,n,(i,j) -> 1/(3^i+3^j));
  denom(LinearAlgebra:-Determinant(M))
end proc:
map(g, [$1..10]);

a(n) = denominator(matdet(matrix(n, n, i, j, 1/(3^i+3^j)))); \\ Michel Marcus, Jan 06 2025

A069741 Let M_n be the n X n matrix M_(i,j)=1/(2^i+2^j), then a(n) is the numerator of det(M_n).

Original entry on oeis.org

1, 1, 1, 49, 2401, 113060689, 260871824431729, 9708455965188246321478801, 361304320362377236050632364626862769, 3511057522394397982450601057907077808699210592028881

Offset: 1

Benoit Cloitre, Apr 21 2002

a(n) seems always to be a square and 7 seems to follow a rule in a(n) factorization. Maximal k such that 7^k divides a(n) are 0, 0, 0, 2, 4, 6, 10, 14, 18, 24, 30, 36, 44, 52, 60, 70, 80, 90, 102, 114, 126, 142, 158, 174, 192... Hence if b(n)=maximum exponent of 7 in factorization of a(n), b(3n+1)=A049450(n); b(3n+2)=A049450(n)+2*n; b(3n+3)=A049450(n)+4n

Vincenzo Librandi, Table of n, a(n) for n = 1..25

Cf. A069743.

for(n=1,70,print1(numerator(matdet(matrix(n,n,i,j,1/(2^i+2^j)))),","))

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A069742 Duplicate of A069743.

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A379913 Let M_n be the n X n matrix M_(i,j)=1/(3^i+3^j), then a(n) is the denominator of det(M_n).

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A069741 Let M_n be the n X n matrix M_(i,j)=1/(2^i+2^j), then a(n) is the numerator of det(M_n).

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