A356371 - OEIS

%I #36 Oct 27 2023 19:34:18

%S 1,2,3,8,15,24,35,48,63,270,440,528,780,1078,2925,1440,8160,2142,5472,

%T 34560,23919,235598,64239,42480,158400,1255800,1614600,1247400,

%U 16442971,8233650,41021370,21561120,127327167,439824000,439824000,24504444,1329112224,1653775162

%N a(n) is the smallest positive integer k, such that set of pairwise gcd of k, k+1, ..., k+n has a cardinality of n.

%C n | a(n). - _David A. Corneth_, Oct 17 2022

%H Giovanni Resta, <a href="/A356371/b356371.txt">Table of n, a(n) for n = 1..60</a> (first 42 terms from Chai Wah Wu)

%t a[n_] := Module[{k = 1}, While[Length[Union[GCD @@@ Subsets[k + Range[0, n], {2}]]] != n, k++]; k]; Array[a, 20] (* _Amiram Eldar_, Oct 17 2022 *)

%o (Python)

%o from math import gcd

%o from itertools import count

%o def A356371(n):

%o     for k in count(n,n):

%o         if len(set(gcd(i,j) for i in range(k,n+k+1) for j in range(i+1,n+k+1))) == n:

%o             return k # _Chai Wah Wu_, Oct 18 2022

%Y Cf. A214799.

%K nonn

%O 1,2

%A _Gleb Ivanov_, Oct 17 2022

%E a(31)-a(38) from _Giovanni Resta_, Oct 17 2022