A071809 Smallest number s such that s*k-1 is squarefree for 1 <= k <= n.

2, 2, 2, 2, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 24, 120, 120, 120, 120, 120, 150, 150, 150, 150, 240, 240, 240, 240, 240, 240, 300, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840, 840

Offset

1,1

Comments

a(n) is even for all n. - Amiram Eldar, Apr 30 2025

Links

Amiram Eldar, Table of n, a(n) for n = 1..533

Formula

From Amiram Eldar, Apr 30 2025: (Start)

a(n) >= a(n-1) for n >= 2.

a(n) = A383547(m), for n = A383548(m-1)+1..A383548(m), m >= 2. (End)

Mathematica

a[n_] := a[n] = Module[{s = 2, m = n + 1}, While[! AllTrue[s*Range[n] - 1, SquareFreeQ], s += 2]; While[SquareFreeQ[s*m - 1], a[m] = s; m++]; s]; Array[a, 60] (* Amiram Eldar, Apr 30 2025 *)

Prog

(PARI) a(n) = my(s=1); while(sum(i=1, n, issquarefree(s*i-1))<n, s++); s;

Crossrefs

Cf. A005117, A383546, A383547, A383548.

Sequence in context: A239494 A349388 A347663 * A347325 A324762 A104976

Adjacent sequences: A071806 A071807 A071808 * A071810 A071811 A071812

Keyword

nonn

Author

Benoit Cloitre, Jun 06 2002

Status

approved