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A273820
Least common multiple of (2^n, 2^n + 1, ..., 2^(n+1) - 1).
1
1, 6, 420, 360360, 72201776446800, 591133442051411133755680800, 6676878045498705789701874602220118271269436344024536000
OFFSET
0,2
COMMENTS
From David Trimas, Sep 17 2024: (Start)
a(n) is the product of the maximal prime powers below 2^(n+1) - 1.
Example: For n=3 the maximal prime powers below 2^(3+1) - 1 = 15 are 2^3, 3^2, 5^1, 7^1, 11^1, 13^1 and their product is 8*9*5*7*11*13 = 360360. (End)
FORMULA
a(n) = A003418(2^(n+1)-1) - David Trimas, Sep 23 2024
MATHEMATICA
Table[LCM@@Table[2^n+i, {i, 0, 2^n-1}], {n, 0, 7}] (* Waldemar Puszkarz, May 31 2016 *)
a273820[n_] := Times @@ (Times @@ Prime@Range@PrimePi@(2^(((n + 1)/#))) & /@ Range[n])
Table[a273820[n], {n, 0, 15}] (* David Trimas, Sep 23 2024 *)
PROG
(Sage) [lcm([2^n+i for i in [0..2^n-1]]) for n in [0..10]] # Tom Edgar, May 31 2016
(PARI) a(n)=lcm([2^n..2^(n+1)-1]) \\ Charles R Greathouse IV, Jun 08 2016
CROSSREFS
Sequence in context: A174773 A229471 A258192 * A162088 A199253 A199198
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, May 31 2016
STATUS
approved