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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Avery Diep

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

Original entry on oeis.org

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

Author

Avery Diep, Jun 24 2025

Keywords

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).

Examples

			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.
		

Programs

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

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).