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

Éric Angelini bk263401 at skynet.be
Mon May 13 11:42:51 CEST 2019

```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.

```