A331953 a(n) is the least positive k such that floor(n/k) is a square number.

1, 1, 2, 2, 1, 3, 4, 4, 2, 1, 6, 6, 3, 3, 3, 8, 1, 4, 2, 2, 5, 5, 5, 5, 5, 1, 6, 3, 3, 3, 7, 7, 2, 2, 7, 8, 1, 4, 4, 4, 9, 9, 9, 9, 9, 5, 5, 5, 3, 1, 2, 2, 11, 11, 6, 6, 6, 6, 6, 6, 13, 13, 13, 7, 1, 4, 4, 4, 7, 7, 15, 15, 2, 2, 8, 3, 3, 3, 8, 8, 5, 1, 5, 5, 5

Offset

0,3

Comments

This sequence is unbounded; a(n!*p) > n where p is a prime number > n.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Formula

a(n^2) = 1.

a(2*n^2) = 2 for any n > 0.

Example

For n = 12:
- floor(13/1) = 13 is not a square number,
- floor(13/2) = 6 is not a square number,
- floor(13/3) = 4 is a square number,
- hence a(13) = 3.

Mathematica

Array[Block[{k = 1}, While[! IntegerQ@ Sqrt@ Floor[#/k], k++]; k] &, 85, 0] (* Michael De Vlieger, Feb 04 2020 *)

Prog

(PARI) a(n) = for (k=1, oo, if (issquare(n\k), return (k)))

Crossrefs

Cf. A331954 (prime variant), A331958 (corresponding square roots), A332012 (corresponding squares).

Sequence in context: A216368 A123956 A368606 * A113594 A368604 A246425

Adjacent sequences: A331950 A331951 A331952 * A331954 A331955 A331956

Keyword

nonn

Author

Rémy Sigrist, Feb 02 2020

Status

approved