A383546 a(n) is the largest number k such that i*n - 1 is squarefree for all 1 <= i <= k, or 0 if no such number exists.

0, 4, 2, 6, 0, 20, 2, 7, 0, 0, 2, 22, 0, 1, 2, 3, 0, 6, 0, 4, 0, 6, 1, 23, 0, 0, 2, 0, 0, 17, 2, 1, 0, 3, 2, 14, 0, 1, 2, 6, 0, 2, 2, 3, 0, 0, 2, 11, 0, 0, 0, 3, 0, 9, 0, 4, 0, 4, 1, 8, 0, 7, 1, 0, 0, 10, 2, 1, 0, 3, 2, 7, 0, 1, 2, 0, 0, 16, 2, 7, 0, 0, 2, 13, 0

Offset

1,2

Comments

The sums of the first 10^k terms, for k = 1, 2, ..., are 41, 313, 2942, 28825, 284800, 2844262, 28423972, 284178338, 2841613719, 28416262298, ... . Apparently, the asymptotic mean of this sequence is 2.8416..., which seems to be also the asymptotic mean of A383543.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = 0 if and only if n = 1 or n-1 is nonsquarefree (A013929).

Mathematica

a[n_] := Module[{k = 1, s = n-1}, While[SquareFreeQ[s], s += n; k++]; k-1]; Array[a, 100]

Prog

(PARI) a(n) = {my(k = 1, s = n-1); while(issquarefree(s), s += n; k++); k-1; }

Crossrefs

Cf. A005117, A013929, A071809, A383543, A383547 (indices of records), A383548 (record values).

Sequence in context: A178394 A266391 A091664 * A378328 A010317 A358200

Adjacent sequences: A383543 A383544 A383545 * A383547 A383548 A383549

Keyword

nonn,easy

Author

Amiram Eldar, Apr 30 2025

Status

approved