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URL: https://oeis.org/A056604

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A056604
a(0)=1; thereafter a(n) = lcm(1, 2, 3, 4, ..., prime(n)).
9
1, 2, 6, 60, 420, 27720, 360360, 12252240, 232792560, 5354228880, 2329089562800, 72201776446800, 5342931457063200, 219060189739591200, 9419588158802421600, 442720643463713815200, 164249358725037825439200, 9690712164777231700912800, 591133442051411133755680800
OFFSET
0,2
COMMENTS
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
a(342) has 1000 decimal digits. - Michael De Vlieger, Mar 05 2017
LINKS
Thomas Bloom, Problem 458, Erdős Problems.
Erdős problems database contributors, Erdős problem database, see no. 458.
FORMULA
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
a(n) = A003418(prime(n)). - M. F. Hasler, Jan 04 2020
EXAMPLE
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.
MAPLE
a:= n-> ilcm($1..`if`(n=0, 0, ithprime(n))):
seq(a(n), n=0..20); # Alois P. Heinz, Dec 05 2014
MATHEMATICA
Table[If[n == 0, 1, LCM @@ Range@ Prime@ n], {n, 0, 18}] (* Michael De Vlieger, Mar 05 2017 *)
PROG
(PARI) a(n)=lcm(vector(prime(n), i, i)) \\ Charles R Greathouse IV, Oct 27 2013
(PARI) apply( A056604(n)=lcm([2..if(n, prime(n))]), [0..20]) \\ Or A056604(n) = A003418(prime(n)), might be more efficient. - M. F. Hasler, Jan 04 2020
(Magma) [1] cat [Lcm([2..p]): p in PrimesUpTo(65)]; // Bruno Berselli, Feb 08 2015
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Labos Elemer, Aug 07 2000
EXTENSIONS
a(16) from Frank Ellermann, Dec 18 2001
New name from Charles R Greathouse IV, Oct 27 2013
More terms from Alois P. Heinz, Dec 05 2014
a(0)=1 added to definition by N. J. A. Sloane, Jan 05 2020
STATUS
approved