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

1,2

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)

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 *)

Prog

(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

Crossrefs

Cf. A214799.

Sequence in context: A122412 A365413 A174019 * A293389 A128035 A003473

Adjacent sequences: A356368 A356369 A356370 * A356372 A356373 A356374

Keyword

nonn

Author

Gleb Ivanov, Oct 17 2022

Extensions

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

Status

approved