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A084190
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Least common multiple of {d-1: d > 1 and d divides n}.
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3
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1, 1, 2, 3, 4, 10, 6, 21, 8, 36, 10, 330, 12, 78, 28, 105, 16, 680, 18, 684, 60, 210, 22, 53130, 24, 300, 104, 702, 28, 36540, 30, 3255, 160, 528, 204, 157080, 36, 666, 228, 62244, 40, 31980, 42, 9030, 616, 990, 46, 2497110, 48, 3528, 400, 5100, 52, 468520
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OFFSET
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1,3
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COMMENTS
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Considering the set of divisors > 1 of n reduced by 1, a(n) is the smallest number whose divisors contain this set;
a(n) is odd iff n=2^k.
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LINKS
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EXAMPLE
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n=35: divisors > 1 of 35 = {5,7,35}, a(35) = lcm(4,6,34) = 204;
n=37: divisors > 1 of 37 = {37}, a(37) = lcm(36) = 36.
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MATHEMATICA
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Join[{1}, Table[LCM @@ (Rest[Divisors[n]] - 1), {n, 2, 100}]] (* T. D. Noe, Apr 25 2012 *)
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PROG
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(Haskell)
a084190 1 = 1
a084190 n = foldl1 lcm $ map (subtract 1) $ tail $ a027750_row' n
(Python)
from math import lcm
from sympy import divisors
def A084190(n): return lcm(*(d-1 for d in divisors(n, generator=True) if d > 1)) # Chai Wah Wu, Jun 25 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(45) was erroneously split into 61 and 6; repaired by Carl R. White, Apr 25 2012
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STATUS
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approved
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