OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..100
Gert Almkvist, Powers of a matrix with coefficients in a Boolean ring, Proc. Amer. Math. Soc. 53 (1975), 27-31. See v_n.
J. B. Marshall, On the extension of Fermat's theorem to matrices of order n, Proceedings of the Edinburgh Mathematical Society 6 (1939) 85-91. See (10) page 90 for p=2.
MathOverflow, Do we know any bound on lcm(2^1-1, 2^2-1, ..., 2^n-1)?
FORMULA
a(n) = lcm(1, 3, 7, ..., 2^n - 1).
a(n) = Product_{k=1..n} Phi_k(2), where Phi_n(2) is n-th cyclotomic polynomial at x=2 (cf. A019320). - Vladeta Jovovic, Jan 20 2002
EXAMPLE
a(3) = lcm(1,3,7) = 21.
MAPLE
a:= proc(n) option remember; `if`(n=1, 1, ilcm(a(n-1), 2^n-1)) end:
seq(a(n), n=1..20); # Alois P. Heinz, Oct 16 2011
MATHEMATICA
Table[LCM @@ (2^Range[n] - 1), {n, 1, 20}] (* Jean-François Alcover, Apr 02 2015 *)
PROG
(PARI) A034268(n) = {local(r); r=1; for(k=1, n, r=lcm(r, 2^k-1)); r} \\ Michael B. Porter, Mar 02 2010
(PARI) a(n) = lcm(vector(n, k, 2^k-1)); \\ Michel Marcus, Jul 29 2022
(Magma) [Lcm([2^k-1:k in [1..n]]): n in [1..17]]; // Marius A. Burtea, Jan 29 2020
(Python)
from math import lcm
from itertools import accumulate
def aupto(n): return list(accumulate((2**k-1 for k in range(1, n+1)), lcm))
print(aupto(17)) # Michael S. Branicky, Jul 04 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Apr 20 2000
STATUS
approved