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

Lars Blomberg larsl.blomberg at comhem.se
Wed May 15 16:44:39 CEST 2019

```Hello SeqFans,

For n=6 I get 1 2 3 4 6 8 (same as reported by Peter Munn).
For n=13 I get
1 2 3 4 5 6 7 8 9 15 360 840 1260   sum 2520 not
1 2 3 4 5 6 7 8 10 24 70 280 420 sum 840.
This illustrates a problem with lexicofirst: One can obtain a smaller value for some term, at the expense of larger values for subsequent terms, and a larger sum.
So can one put a limit on the sums to be tested?

/Lars B

-----Ursprungligt meddelande-----
Från: SeqFan <seqfan-bounces at list.seqfan.eu> För Éric Angelini
Skickat: den 13 maj 2019 11:43
Till: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Ämne: [seqfan] 10 integers dividing the sum of the 10 integers

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.

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