

A327271


Smallest modulus of any n X n integer determinant whose top row has all 1's and whose rows are pairwise orthogonal.


4



1, 2, 6, 8, 40, 48, 336, 128, 864, 1280, 8448, 3072, 39936
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

a(n) = A327267(2^n), since 2^n = (p_1)^n is the Heinz code for the multiset {1,1,...,1}.
See Pinner and Smyth link below for more details, including an algorithm for computing A327267(n). Also, see file link below for {(n, a(n), matrix(n)), n <= 13}, where matrix(n) has minimal modulus determinant equal to a(n) among n X n matrices with top row all 1's and all rows orthogonal.
For the first 13 terms, the number of prime factors counted with multiplicity equals n1: A001222(a(n))=n1. How far does this hold?  Jon Maiga, Sep 07 2019


LINKS

Table of n, a(n) for n=1..13.
Chris Pinner and Chris Smyth, Lattices of minimal index in Z^n having an orthogonal basis containing a given basis vector
Christopher J. Smyth, List of n, a(n) and associated matrix for n up to 13


EXAMPLE

a(3) = 6 because the matrix [[1,1,1],[1,1,0],[1,1,2]] has top row of 3 1's and all rows orthogonal, and minimal positive determinant equal to 6.


CROSSREFS

Subsequence of A327267, see comments; A327273 is similar, but determinant's top row is 1,2,2^2,...,2^{n1}.
Sequence in context: A235320 A152158 A291782 * A095239 A192009 A065953
Adjacent sequences: A327268 A327269 A327270 * A327272 A327273 A327274


KEYWORD

nonn,more


AUTHOR

Christopher J. Smyth, Sep 02 2019


STATUS

approved



