# [seqfan] Re: 10 integers dividing the sum of the 10 integers

M. F. Hasler seqfan at hasler.fr
Wed May 15 20:08:29 CEST 2019

```I don't get it, isn't this A081512 as pointed out by Hans on the same day
as the O.P., or is it?

- Maximilian

On Wed, May 15, 2019, 11:46 Neil Sloane <njasloane at gmail.com> wrote:

> We had better say "positive", otherwise {-1,1} is a solution for n=2
>
> Certainly add this to the OEIS, with offset 3,
> S = 6, 12, 24, 60, 60, 60, 180, 420, 420, 840, 840,...
> or maybe, better,
> S = 1, -1, 6, 12, 24, 60, 60, 60, 180, 420, 420, 840, 840,...
> with offset 1, adding "or -1 if there is no solution in positive integers.
>
> You should add the triangle too: Irregular triangle read by rows: row n
> gives [lex .......], or -1 if there is no solution:
>
>  1
>  -1
>  1 2 3
>  1 2 3 6
>  1 2 3 6 12
>  1 2 3 4 20 30
>  1 2 3 4 5 15 30   ...
>
> Best regards
> Neil
>
>
> On Mon, May 13, 2019 at 6:14 AM Éric Angelini <bk263401 at skynet.be> wrote:
>
> > Hello SeqFans,
> > this was suggested to me by an "Enigma" posted here :
> > https://bit.ly/2Vyu9Mv
> >
> > "Find 10 different integers {a, b, c, ... i, j} such
> > that they all divide the sum (a+b+c+d+e+f+g+h+i+j)"
> >
> > The given solution was not mine -- as I wanted to
> > find the lexicographically earliest set of this kind.
> >
> > Then I started to search for such lexico-sets of
> > size "n" (with n > 2). Carole Dubois and I found:
> >
> > n=3, integers = 1 2 3
> > n=4, integers = 1 2 3 6
> > n=5, integers = 1 2 3 6 12
> > n=6, integers = 1 2 3 4 20 30
> > n=7, integers = 1 2 3 4 5 15 30
> > n=8, integers = 1 2 3 4 5 10 15 20
> > n=9, integers = 1 2 3 4 5 6 9 60 90
> > n=10, integers = 1 2 3 4 5 6 7 42 140 210
> > n=11, integers = 1 2 3 4 5 6 7 12 30 140 210
> > n=12, integers = 1 2 3 4 5 6 7 8 20 84 280 420
> > n=13, integers = 1 2 3 4 5 6 7 8 10 24 70 280 420
> >
> > We stopped there.
> >
> > Questions:
> > Could someone (if this is of interest and not old hat)
> > extend this array to, say, n = 100?
> > And how could this array enter the OEIS?
> > Carine said to me that the successive row-sums might be
> > a possibility. We would then have this 11-term start:
> >
> > S = 6, 12, 24, 60, 60, 60, 180, 420, 420, 840, 840,...
> > (this succession is not in the OEIS)
> >
> > Best,
> > É.
>

```