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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.

%I A334352 #24 Aug 03 2020 01:11:16
%S A334352 1,6,15,14,18,22,26,26,34,38,38,29,29,29,29,37,41,43,43,43,43,47,47,
%T A334352 47,47,47,59,59,59,59,61,71,71,71,77,79,79
%N 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.
%C A334352 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.
%H A334352 Zizheng Fang, <a href="/A334352/a334352.txt">Python program to generate A334352</a>
%e A334352 n=1:
%e A334352 1
%e A334352 n=2:
%e A334352 3, 6
%e A334352 3*6 = 18
%e A334352 3+6 divides 18
%e A334352 n=3:
%e A334352 3, 12, 15
%e A334352 3*12*15 = 540
%e A334352 3+12 divides 540
%e A334352 3+15 divides 540
%e A334352 12+15 divides 540
%e A334352 n=4:
%e A334352 2, 6, 10, 14
%e A334352 2*6*10*14 = 1680
%e A334352 2+6 divides 1680
%e A334352 2+10 divides 1680
%e A334352 2+14 divides 1680
%e A334352 6+10 divides 1680
%e A334352 6+14 divides 1680
%e A334352 10+14 divides 1680
%e A334352 n=5:
%e A334352 2, 6, 10, 14, 18
%e A334352 n=6:
%e A334352 2, 6, 10, 14, 18, 22
%e A334352 n=7:
%e A334352 2, 4, 10, 14, 18, 22, 26
%e A334352 2, 6, 10, 14, 18, 22, 26
%e A334352 4, 6, 10, 14, 18, 22, 26
%e A334352 n=8:
%e A334352 2, 4, 6, 10, 14, 18, 22, 26
%e A334352 n=9:
%e A334352 2, 6, 8, 10, 14, 18, 22, 26, 34
%e A334352 2, 6, 10, 14, 18, 22, 26, 30, 34
%Y A334352 Cf. A334354.
%K A334352 nonn,more
%O A334352 1,2
%A A334352 _Zizheng Fang_, Apr 24 2020