A056167 Numbers k such that k! is not divisible by the square of (f+1)!, where f = floor(k/2).

2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79

Offset

1,1

Comments

Values of f are in A001057 or A004526.

Numbers k such that for some prime p, Sum_{i>=1} (floor(k/p^i) - 2 * floor((f+1)/p^i)) < 0, where f = floor(k/2). - Robert Israel, Oct 14 2024

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

12 is a term because 12!/(7!*7!) = 132/7 is not an integer.
10 is not a term because 10!/(6!*6!) = 7 is an integer.

Maple

filter:= k -> k!  mod ((1+floor(k/2))!)^2 <> 0:
select(filter, [$1..100]); # Robert Israel, Oct 13 2024

Mathematica

q[k_] := !Divisible[k!, (Floor[k/2] + 1)!^2]; Select[Range[100], q] (* Amiram Eldar, Mar 17 2025 *)

Prog

(PARI) isok(k) = k! % ((k\2)+1)!^2; \\ Amiram Eldar, Mar 17 2025

Crossrefs

Cf. A001057, A004526.

Complement of A056167.

Sequence in context: A163807 A118766 A136399 * A050759 A039274 A102487

Adjacent sequences: A056164 A056165 A056166 * A056168 A056169 A056170

Keyword

nonn

Author

Labos Elemer, Jul 27 2000

Status

approved