Search: id:A048671
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%I A048671
%S A048671 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,
%T A048671 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,
%U A048671 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
%N A048671 a(n) = q(n)/q(n-1), where q(n) = n!/A003418(n).
%C A048671 a(n) is the lcm of the proper divisors of n. - David Wasserman (wasserma(AT)spawar.navy.mil), 
               Nov 30 2004
%C A048671 a(n) = (n^2)/A140580. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 17 
               2008
%H A048671 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SylvesterCyclotomicNumber.html">Sylvester Cyclotomic Number</a>
%H A048671 <a href="Sindx_Lc.html#lcm">Index entries for sequences related to lcm's</
               a>
%F A048671 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).
%F A048671 Also a(n)=A003418(n)/A002944(n)=LCM[1, .., n]/LCM[.., C[n, j], ..].
%F A048671 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
%F A048671 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
%F A048671 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
%e A048671 8!/LCM(8) = 48 = 40320/840 while 7!/LCM(7) = 5040/420 = 12 so a(8) = 
               48/12 = 4.
%e A048671 a(5)=1=LCM[1,2,3,4,5]/LCM[1,5,10,10,5,1]
%Y A048671 Cf. A025527, A003418, A002944, A000142, A014963.
%Y A048671 Cf. A140580.
%Y A048671 Sequence in context: A082388 A085099 A154744 this_sequence A088123 A050932 
               A166120
%Y A048671 Adjacent sequences: A048668 A048669 A048670 this_sequence A048672 A048673 
               A048674
%K A048671 nonn
%O A048671 1,4
%A A048671 Labos E. (labos(AT)ana.sote.hu)

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