A331954 - OEIS

A331954

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

1, 1, 2, 1, 2, 1, 3, 3, 2, 1, 4, 1, 2, 2, 3, 1, 5, 1, 4, 3, 2, 1, 7, 5, 2, 2, 4, 1, 4, 1, 6, 3, 2, 2, 5, 1, 2, 2, 3, 1, 6, 1, 4, 4, 2, 1, 9, 7, 7, 3, 3, 1, 4, 4, 5, 3, 2, 1, 8, 1, 2, 2, 9, 5, 5, 1, 4, 3, 3, 1, 10, 1, 2, 2, 4, 4, 4, 1, 6, 6, 2, 1, 11, 5, 2, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,3

COMMENTS

This sequence is unbounded; a(n!*p^2) > n where n > 1 and p is a prime number > n.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 2..10000

FORMULA

a(n) = 1 iff n is a prime number.

EXAMPLE

For n = 8:

- floor(8/1) = 8 is not a prime number,

- floor(8/2) = 4 is not a prime number,

- floor(8/3) = 2 is a prime number,

- hence a(8) = 3.

MATHEMATICA

Array[Block[{k = 1}, While[! PrimeQ@ Floor[#/k], k++]; k] &, 86, 2] (* Michael De Vlieger, Feb 04 2020 *)

PROG

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

CROSSREFS

Cf. A331953 (square variant), A331959 (corresponding prime numbers).

Sequence in context: A322866 A328847 A331175 * A309892 A078899 A055172

Adjacent sequences: A331951 A331952 A331953 * A331955 A331956 A331957

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Feb 02 2020

STATUS

approved