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Search: id:A048671
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| 1, 1, 1, 2, 1, 6, 1, 4, 3, 10, 1, 12, 1, 14, 15, 8, 1, 18, 1, 20, 21, 22, 1, 24, 5, 26, 9, 28, 1, 30, 1, 16, 33, 34, 35, 36, 1, 38, 39, 40, 1, 42, 1, 44, 45, 46, 1, 48, 7, 50, 51, 52, 1, 54, 55, 56, 57, 58, 1, 60, 1, 62, 63, 32, 65, 66, 1, 68, 69, 70, 1, 72, 1, 74, 75, 76, 77, 78, 1
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n) is the lcm of the proper divisors of n. - David Wasserman (wasserma(AT)spawar.navy.mil), Nov 30 2004
a(n) = (n^2)/A140580. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 17 2008
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LINKS
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Eric Weisstein's World of Mathematics, Sylvester Cyclotomic Number
Index entries for sequences related to lcm's
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FORMULA
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A025527(n)/A025527(n-1) or (n*LCM(n-1))/LCM(n) where LCM(n) is least common multiple of first n natural numbers: LCM(n) = A003418(n).
Also a(n)=A003418(n)/A002944(n)=LCM[1, .., n]/LCM[.., C[n, j], ..].
a(n) = n/A014963(n) = LCM(A052126(n), A032742(n)); a(n) = n if n not a prime power, a(n) = n/p if n = p^m (i.e. a(n) = 1 if n = p) - Henry Bottomley (se16(AT)btinternet.com), May 19 2000
a(n) = n*Product_{ d divides n } d^mu(d). Product_{ d divides n } a(d) = A007956(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 04 2002
a(n)=product{k=1..n-1, if(gcd(n, k)>1, 1-exp(2*pi*I*k/n), 1)}, I=sqrt(-1); - Paul Barry (pbarry(AT)wit.ie), Apr 15 2005
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EXAMPLE
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8!/LCM(8) = 48 = 40320/840 while 7!/LCM(7) = 5040/420 = 12 so a(8) = 48/12 = 4.
a(5)=1=LCM[1,2,3,4,5]/LCM[1,5,10,10,5,1]
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CROSSREFS
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Cf. A025527, A003418, A002944, A000142, A014963.
Cf. A140580.
Sequence in context: A082388 A085099 A154744 this_sequence A088123 A050932 A166120
Adjacent sequences: A048668 A048669 A048670 this_sequence A048672 A048673 A048674
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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