A385302 Least common multiple of {n^n-1, n^(n-1)-1, ..., n-1}.

1, 0, 3, 104, 5355, 15107664, 2684295425, 2261529015616800, 97901171532649325295, 671549787473885210310580160, 113480471243172592617657936025689, 67423693602852027222491606156048516615143200, 52627558956534012662100374980910169826998422190695

Offset

0,3

Comments

For prime powers q (i.e. A000961), A351657(q) divides q*a(q). Follows from Niven's Fermat's theorem for matrices when considering Fibonacci q-step matrices over GF(q).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..44

Ivan Niven, Fermat’s theorem for matrices, Duke Math. J., Vol. 15, No. 3 (1948), pp. 823-826.

Formula

a(n) = LCM{n^n-1, n^(n-1)-1, ..., n-1}.

Conjecture: a(n) = Product_{k=1..n} Cyclotomic[k, n], i.e., a(n) = A156291(A000217(n)-1).

Example

a(1) = LCM{1-1} = 0, a(2) = LCM{2^2-1,2-1} = 3, a(3) = LCM{3^3-1,3^2-1,3-1} = 104.

Maple

a:= n-> ilcm(n^j-1$j=1..n):
seq(a(n), n=0..12);  # Alois P. Heinz, Jun 25 2025

Mathematica

a[n_] := LCM @@ (n^Range[n] - 1); a[0] = 1; Array[a, 14, 0] (* Amiram Eldar, Jun 25 2025 *)

Prog

(PARI) a(n) = lcm(vector(n, k, n^k-1)); \\ Michel Marcus, Jun 25 2025

Crossrefs

Cf. A000217, A000961, A003418, A048861, A156291, A351657.

Sequence in context: A241348 A050651 A233251 * A279303 A385833 A103037

Adjacent sequences: A385299 A385300 A385301 * A385303 A385304 A385305

Keyword

nonn

Author

Avery Diep, Jun 24 2025

Status

approved