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A356371 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.

%I A356371 #36 Oct 27 2023 19:34:18
%S A356371 1,2,3,8,15,24,35,48,63,270,440,528,780,1078,2925,1440,8160,2142,5472,
%T A356371 34560,23919,235598,64239,42480,158400,1255800,1614600,1247400,
%U A356371 16442971,8233650,41021370,21561120,127327167,439824000,439824000,24504444,1329112224,1653775162
%N A356371 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 A356371 n | a(n). - _David A. Corneth_, Oct 17 2022
%H A356371 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 A356371 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 A356371 (Python)
%o A356371 from math import gcd
%o A356371 from itertools import count
%o A356371 def A356371(n):
%o A356371     for k in count(n,n):
%o A356371         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 A356371             return k # _Chai Wah Wu_, Oct 18 2022
%Y A356371 Cf. A214799.
%K A356371 nonn
%O A356371 1,2
%A A356371 _Gleb Ivanov_, Oct 17 2022
%E A356371 a(31)-a(38) from _Giovanni Resta_, Oct 17 2022