A360825 a(n) is the remainder after dividing n! by its least nondivisor.

1, 1, 2, 2, 4, 1, 6, 2, 5, 1, 10, 1, 12, 3, 8, 1, 16, 1, 18, 4, 11, 1, 22, 22, 6, 5, 14, 1, 28, 1, 30, 33, 20, 31, 18, 1, 36, 7, 20, 1, 40, 1, 42, 8, 23, 1, 46, 19, 11, 9, 26, 1, 52, 30, 27, 10, 29, 1, 58, 1, 60, 43, 53, 56, 33, 1, 66, 12, 35, 1, 70, 1, 72, 27, 23

Offset

0,3

Comments

For every term besides a(3), the least nondivisor is the next prime after n.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

a(n) = 1 <=> n in { A040976 } \ { 3 }.

a(n) = n <=> n in { A006093 }.

a(n) = n! mod A151800(n) for n > 3.

a(n) = A213636(n!) = A213636(A000142(n)).

a(A000040(n)) = A275111(n) for n >= 3.

a(n) > n <=> n in { A360805 }.

Example

a(5) = 5! mod 7 = 120 mod 7 = 1.

Mathematica

a[n_] := Module[{f = n!, m = n + 1}, While[Divisible[f, m], m++]; Mod[f, m]]; Array[a, 100, 0] (* Amiram Eldar, Feb 22 2023 *)

Prog

(PARI) a(n) = my(k=1, r); while(!(r=(n! % (n+k))), k++); r; \\ Michel Marcus, Feb 22 2023
(Python)
from functools import reduce
from sympy import nextprime
def A360825(n):
    if n == 3: return 2
    m = nextprime(n)
    return reduce(lambda i, j: i*j%m, range(2, n+1), 1)%m # Chai Wah Wu, Feb 22 2023
(Python)
from functools import reduce
from sympy import nextprime
def A360825(n):
    if n == 3: return 2
    m = nextprime(n)
    return (m-1)*pow(reduce(lambda i, j:i*j%m, range(n+1, m), 1), -1, m)%m # Chai Wah Wu, Feb 23 2023

Crossrefs

Cf. A000040, A000142, A006093, A040976, A151800, A213636, A275111, A360805.

Sequence in context: A116588 A069922 A072211 * A328925 A299020 A343505

Adjacent sequences: A360822 A360823 A360824 * A360826 A360827 A360828

Keyword

nonn

Author

Sebastian F. Orellana, Feb 22 2023

Status

approved