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A208570
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LCM of n and smallest nondivisor of n.
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2
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2, 6, 6, 12, 10, 12, 14, 24, 18, 30, 22, 60, 26, 42, 30, 48, 34, 36, 38, 60, 42, 66, 46, 120, 50, 78, 54, 84, 58, 60, 62, 96, 66, 102, 70, 180, 74, 114, 78, 120, 82, 84, 86, 132, 90, 138, 94, 240, 98, 150, 102, 156, 106, 108, 110, 168, 114, 174, 118, 420, 122
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OFFSET
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1,1
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COMMENTS
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a(n) = 2*n for all odd numbers.
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LINKS
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FORMULA
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For primes p let nu_p(n) be the p-adic order of n.
a(n) = p * n where p is the prime that minimizes p^(1+nu_p(n)). (End)
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EXAMPLE
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a(6) = 12 because the divisors of 6 are 1,2,3,6; 4 is the smallest number not a divisor of 6; the LCM of 6 and 4 is 12.
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MAPLE
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a:= proc(n) local t;
for t from 2 do
if irem (n, t)<>0 then return ilcm(t, n) fi
od
end:
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MATHEMATICA
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Table[LCM[n, Min[Complement[Range[n + 1], Divisors[n]]]], {n, 61}] (* Ivan Neretin, May 20 2015 *)
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PROG
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(Haskell)
(PARI) a(n) = {my(k=2); while(!(n % k), k++); lcm(n, k); } \\ Michel Marcus, Mar 13 2018
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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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STATUS
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approved
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