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A064446
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GCD[n!, n^n, LCM[1...n]], or GCD[n^n, LCM[1...n]].
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1
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1, 2, 3, 4, 5, 12, 7, 8, 9, 40, 11, 72, 13, 56, 45, 16, 17, 144, 19, 80, 63, 176, 23, 144, 25, 208, 27, 112, 29, 10800, 31, 32, 297, 544, 175, 864, 37, 608, 351, 800, 41, 6048, 43, 352, 675, 736, 47, 864, 49, 800, 459, 416, 53, 864, 275, 1568, 513, 928, 59, 21600, 61
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| a(n)=GCD[A000142(n), A000312(n), A003418(n)]= GCD[A000312(n), A003418(n)]=GCD[A051696(n), A003418(n)]
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EXAMPLE
| n=6: a(6)=GCD[720,60,46656]=12
Since only 1 and 5 are relatively prime to 6, a(6) = LCM(1,2,3,4,5,6) / LCM(1,5) = 60/5 = 12.
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MAPLE
| A064446 := n -> ilcm(seq(i, i=1..n))/ilcm(op(select(k->igcd(n, k)=1, [$1..n])));
seq(A064446(i), i=0..61); # Peter Luschny, Jun 25 2011
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MATHEMATICA
| Table[GCD[n!, n^n, LCM@@Range[n]], {n, 70}] (* From Harvey P. Dale, June 25 2011 *)
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PROG
| (PARI) { L=1; for (n=1, 1000, L=lcm(L, n); write("b064446.txt", n, " ", gcd(n^n, L)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 14 2009]
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CROSSREFS
| Cf. A000142, A000312, A051696. Equals A003418(n)/A038610(n).
Sequence in context: A065636 A135323 A052106 * A143482 A193679 A066574
Adjacent sequences: A064443 A064444 A064445 * A064447 A064448 A064449
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Oct 02 2001
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