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.

1, 2, 3, 8, 15, 24, 35, 48, 63, 270, 440, 528, 780, 1078, 2925, 1440, 8160, 2142, 5472, 34560, 23919, 235598, 64239, 42480, 158400, 1255800, 1614600, 1247400, 16442971, 8233650, 41021370, 21561120, 127327167, 439824000, 439824000, 24504444, 1329112224, 1653775162

Offset: 1

Author

Gleb Ivanov, Oct 17 2022

Keywords

• nonn

Comments

n | a(n). - David A. Corneth, Oct 17 2022

Links

• Giovanni Resta, Table of n, a(n) for n = 1..60 (first 42 terms from Chai Wah Wu)

Crossrefs

Cf. A214799.

Programs

Mathematica

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 *)

Python

from math import gcd
from itertools import count
def A356371(n):
    for k in count(n,n):
        if len(set(gcd(i,j) for i in range(k,n+k+1) for j in range(i+1,n+k+1))) == n:
            return k # Chai Wah Wu, Oct 18 2022

Extensions

a(31)-a(38) from Giovanni Resta, Oct 17 2022