A334352 The least positive integer k such that there exists a set of n distinct integers less than or equal to k with this property: the sum of every two members of this set divides the product of all the members of this set.

1, 6, 15, 14, 18, 22, 26, 26, 34, 38, 38, 29, 29, 29, 29, 37, 41, 43, 43, 43, 43, 47, 47, 47, 47, 47, 59, 59, 59, 59, 61, 71, 71, 71, 77, 79, 79

Offset: 1

Author

Zizheng Fang, Apr 24 2020

Keywords

• nonn
• more

Comments

Upper bound: For every n != 3, a(n) <= 4n-2. Proof: For every n >= 5, we have the set {2, 6, 10, ..., 4n-2}, which obviously possesses the desired property. It happens to also work for n = 1, 2, 4.

Examples

			n=1:
1
n=2:
3, 6
3*6 = 18
3+6 divides 18
n=3:
3, 12, 15
3*12*15 = 540
3+12 divides 540
3+15 divides 540
12+15 divides 540
n=4:
2, 6, 10, 14
2*6*10*14 = 1680
2+6 divides 1680
2+10 divides 1680
2+14 divides 1680
6+10 divides 1680
6+14 divides 1680
10+14 divides 1680
n=5:
2, 6, 10, 14, 18
n=6:
2, 6, 10, 14, 18, 22
n=7:
2, 4, 10, 14, 18, 22, 26
2, 6, 10, 14, 18, 22, 26
4, 6, 10, 14, 18, 22, 26
n=8:
2, 4, 6, 10, 14, 18, 22, 26
n=9:
2, 6, 8, 10, 14, 18, 22, 26, 34
2, 6, 10, 14, 18, 22, 26, 30, 34
		

Links

• Zizheng Fang, Python program to generate A334352

Crossrefs

Cf. A334354.