# [seqfan] Re: two dumb questions

David Seal david.j.seal at gwynmop.com
Sun Jul 23 11:58:24 CEST 2017

```I think there is a typo in the A143104 formula: it says that:

a(i,j) = 1 if j=1 or j|i; 0 otherwise.

But https://en.wikipedia.org/wiki/Redheffer_matrix says:

whose entries a(i,j) are 1 if i divides j or if j = 1; otherwise, a(i,j) = 0.

I.e. there's a 'j divides i' vs 'i divides j' difference - and the Wikipedia definition looks more sensible because the alternative 'j=1' condition is completely redundant in the A143104 definition - j always divides i when j=1.

If that's right, the differences between A051731 and A143104 stem from the fact that T(n,k) as defined in A051731 is omitted from the sequence when k > n (since it is always zero in that case, making A051731 a triangle read by rows:

1

1 - 1

1 - 0 - 1

1 - 1 - 0 - 1

1 - 0 - 0 - 0 - 1

1 - 1 - 1 - 0 - 0 - 1

:   :   :   :   :   :   .

while A143104 is the transpose of that triangle with the omitted zeros included, except that the first column is replaced with ones, and read by upwards antidiagonals:

1   1   1   1   1   1
/   /   /   /   /
1   1   0   1   0   1
/   /   /   /
1   0   1   0   0   1
/   /   /
1   0   0   1   0   0
/   /
1   0   0   0   1   0
/
1   0   0   0   0   1

I should add that as this is the first time I remember ever hearing about Redheffer matrices, I'm not 100% certain about it - so it would be good if anyone more expert can confirm or correct my understanding of what's going on here!

Regards,

David

> On 22 July 2017 at 02:43 Peter Lawrence <peterl95124 at sbcglobal.net> wrote:
>
> A051731: characteristic triangle of divisors of n
>
> A000005: = number of divisors of n   =   row sums of A051731
>
> 1.  How is A051731 different from Redheffer matrix A143104,
> which seems to have same FORMULA definition ?
> a(i,j) = 1 if j=1 or j|i; 0 otherwise.
> ...

```