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A034268
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a(n) = LCM_{k=1..n} (2^k - 1).
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5
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1, 3, 21, 105, 3255, 9765, 1240155, 21082635, 1539032355, 16929355905, 34654391537535, 450507089987955, 3690103574091339405, 158674453685927594415, 23959842506575066756665, 6157679524189792156462905, 807093212915080247739749421255
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OFFSET
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1,2
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LINKS
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FORMULA
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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
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EXAMPLE
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a(3) = lcm(1,3,7) = 21.
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MAPLE
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a:= proc(n) option remember; `if`(n=1, 1, ilcm(a(n-1), 2^n-1)) end:
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MATHEMATICA
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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