A069743 Let M_n be the n X n matrix M_(i,j)=1/(3^i+3^j), then a(n) is the numerator of det(M_n).

1, 1, 1, 169, 57122, 1130708969104, 60520841316555286464512, 967474236461016996630647788281821986816, 3959258211397422699939531791736812415390620457773645692928

Offset: 1

Author

Benoit Cloitre, Apr 21 2002

Keywords

• easy
• nonn

Comments

Curiously, sequence seems related to pentagonal (or 5-gonal) or heptagonal (or 7-gonal) numbers. Some primes follow rules in a(n) factorization. If b(n)= exponent of 13 in a(n) factorization: b(n)=0, 0, 0, 2, 4, 6, 10, 14, 18, 24, 30, 36, 44, 52, 60, 70, 80, 90...so b(3n+1)=A049450(n); b(3n+2)=A049450(n)+2*n; b(3n+3)=A049450(n)+4n. If c(n)= exponent of 11 in a(n) factorization: c(n)=4*(0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, ..) so c(5n+1)=4*A000566(n); c(5n+2)=4*(A000566(n)+2n); c(5n+3)=4*(A000566(n)+3n); c(5n+4)=4*(A000566(n)+4n); c(5n+5)=4*(A000566(n)+5n)

Links

• Robert Israel, Table of n, a(n) for n = 1..21

Crossrefs

Cf. A000566, A049450, A379913.

Programs

Maple

f:= proc(n) local M;
  M:= Matrix(n,n,(i,j) -> 1/(3^i+3^j));
  numer(LinearAlgebra:-Determinant(M))
end proc:
map(f, [$1..10]); # Robert Israel, Jan 06 2025

PARI

for(n=1,15,print1((numerator(matdet(matrix(n,n,i,j,1/(3^j+3^i))))),","))