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%I #43 Jul 29 2022 09:51:49
%S 1,3,21,105,3255,9765,1240155,21082635,1539032355,16929355905,
%T 34654391537535,450507089987955,3690103574091339405,
%U 158674453685927594415,23959842506575066756665,6157679524189792156462905,807093212915080247739749421255
%N a(n) = LCM_{k=1..n} (2^k - 1).
%H Alois P. Heinz, <a href="/A034268/b034268.txt">Table of n, a(n) for n = 1..100</a>
%H Gert Almkvist, <a href="https://doi.org/10.1090/S0002-9939-1975-0376713-2">Powers of a matrix with coefficients in a Boolean ring</a>, Proc. Amer. Math. Soc. 53 (1975), 27-31. See v_n.
%H J. B. Marshall, <a href="https://doi.org/10.1017/S0013091500024536">On the extension of Fermat's theorem to matrices of order n</a>, Proceedings of the Edinburgh Mathematical Society 6 (1939) 85-91. See (10) page 90 for p=2.
%H MathOverflow, <a href="http://mathoverflow.net/questions/201757">Do we know any bound on lcm(2^1-1, 2^2-1, ..., 2^n-1)?</a>
%F a(n) = lcm(1, 3, 7, ..., 2^n - 1).
%F 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
%e a(3) = lcm(1,3,7) = 21.
%p a:= proc(n) option remember; `if`(n=1, 1, ilcm(a(n-1), 2^n-1)) end:
%p seq(a(n), n=1..20); # _Alois P. Heinz_, Oct 16 2011
%t Table[LCM @@ (2^Range[n] - 1), {n, 1, 20}] (* _Jean-François Alcover_, Apr 02 2015 *)
%o (PARI) A034268(n) = {local(r);r=1;for(k=1,n,r=lcm(r,2^k-1));r} \\ _Michael B. Porter_, Mar 02 2010
%o (PARI) a(n) = lcm(vector(n, k, 2^k-1)); \\ _Michel Marcus_, Jul 29 2022
%o (Magma) [Lcm([2^k-1:k in [1..n]]): n in [1..17]]; // _Marius A. Burtea_, Jan 29 2020
%o (Python)
%o from math import lcm
%o from itertools import accumulate
%o def aupto(n): return list(accumulate((2**k-1 for k in range(1, n+1)), lcm))
%o print(aupto(17)) # _Michael S. Branicky_, Jul 04 2022
%Y Cf. A003418, A019320, A051844.
%K nonn
%O 1,2
%A _Jeffrey Shallit_, Apr 20 2000
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