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A056604
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a(0)=1; thereafter a(n) = lcm(1, 2, 3, 4, ..., prime(n)).
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9
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1, 2, 6, 60, 420, 27720, 360360, 12252240, 232792560, 5354228880, 2329089562800, 72201776446800, 5342931457063200, 219060189739591200, 9419588158802421600, 442720643463713815200, 164249358725037825439200, 9690712164777231700912800, 591133442051411133755680800
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OFFSET
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0,2
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COMMENTS
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Previous name was: Values of lcm[1,...,m], m = prime, whose squarefree kernels give A002110.
a(n) can be used like A006939(n) for certain kinds of rounding. E.g., the Babylonian a(3) = 60 = 2*2*3*5 divides A006939(3) = 360 = 2*2*2*3*3*5. - Frank Ellermann, Dec 18 2001
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LINKS
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FORMULA
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a(n) = prime(n)^r(n) *...* prime(1)^r(1) for maximal prime(j)^r(j) <= prime(n).
a(n) = Product_{k=1..n} prime(k)^floor(log(prime(n))/log(prime(k))). - Daniel Suteu, Oct 09 2017
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EXAMPLE
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a(5) = lcm(1,2,...,10,11) = 27720, prime(5) = 11. Not all possible lcm(1,..,n) values of A003418 occur, e.g., 12, 840, 25520, etc. are not present. Their squarefree kernels gives exactly A002110.
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MAPLE
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a:= n-> ilcm(`if`(n=0, NULL, $1..ithprime(n))):
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MATHEMATICA
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Table[If[n == 0, 1, LCM @@ Range@ Prime@ n], {n, 0, 18}] (* Michael De Vlieger, Mar 05 2017 *)
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PROG
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(Magma) [1] cat [Lcm([2..p]): p in PrimesUpTo(65)]; // Bruno Berselli, Feb 08 2015
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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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