A390246 a(n) is the least integer k such that there exist n distinct integers b_1, ..., b_n with n < b_i < n+k and b_i is divisible by i for 1 <= i <= n.

2, 3, 4, 6, 6, 9, 9, 11, 13, 15, 15, 17, 16, 19, 20, 25, 24, 27, 26, 29, 30, 31, 30, 33, 36, 38, 40, 43, 42, 46, 45, 50, 49, 48, 50, 55, 54, 55, 58, 60, 59, 61, 60, 62, 66, 67, 66, 73, 72, 77, 76, 79, 78, 82, 82, 89, 88, 87, 86, 91, 90, 89, 98, 105, 104, 103

Offset

1,1

Comments

Erdős and Pomerance ask for an asymptotic formula (see Erdős Problems link).

Links

Sharvil Kesarwani, Table of n, a(n) for n = 1..10000

Thomas Bloom, Problem 710, Erdős Problems.

Example

For n = 4 we need to find the least k such that in (4, 4 + k) there exist 4 distinct integers that are divisible by 1, 2, 3 and 4. This happens for k = 6 and in the interval (4, 10) there exist 4 distinct integers {5, 6, 9, 8} divisible by {1, 2, 3, 4} respectively.

Mathematica

Table[k=n+1; While[Select[Tuples[(v=#; Select[Range[n+1, n+k-1], Mod[#, v]==0&])&/@Range[2, n]], DuplicateFreeQ]=={}, k++]; k, {n, 16}]

Prog

(Python)
from itertools import count, permutations
def A390246(n):
    for k in count(n+1):
        for p in permutations(range(n+1, n+k), r=n-1):
            if not any(p[i-2]%i for i in range(2, n+1)):
                return k # Chai Wah Wu, Nov 10 2025

Crossrefs

Sequence in context: A079667 A073061 A386846 * A300526 A006874 A357476

Adjacent sequences: A390243 A390244 A390245 * A390247 A390248 A390249

Keyword

nonn,nice

Author

Giorgos Kalogeropoulos, Oct 30 2025

Status

approved