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

1,2

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.

Links

Table of n, a(n) for n=1..37.

Zizheng Fang, Python program to generate A334352

Example

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

Crossrefs

Cf. A334354.

Sequence in context: A245200 A070555 A265388 * A128512 A352098 A201142

Adjacent sequences: A334349 A334350 A334351 * A334353 A334354 A334355

Keyword

nonn,more

Author

Zizheng Fang, Apr 24 2020

Status

approved