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 A048671 a(n) is the least common multiple of the proper divisors of n. 16
 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; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A proper divisor d of n is a divisor of n such that 1 <= d < n. Previous name was: a(n) = q(n)/q(n-1), where q(n) = n!/A003418(n). LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 Peter Luschny and Stefan Wehmeier, The lcm(1,2,...,n) as a product of sine values sampled over the points in Farey sequences, arXiv:0909.1838 [math.CA], 2009. Eric Weisstein's World of Mathematics, Sylvester Cyclotomic Number. FORMULA a(n) = A025527(n)/A025527(n-1). a(n) = (n*A003418(n-1))/A003418(n). a(n) = A003418(n-1)/A002944(n). [corrected by Michel Marcus, May 18 2020] From Henry Bottomley, May 19 2000: (Start) 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). (End) From Vladeta Jovovic, Jul 04 2002: (Start) a(n) = n*Product_{d | n} d^mu(d). Product_{d | n} a(d) = A007956(n). (End) a(n) = Product_{k=1..n-1} if(gcd(n, k) > 1, 1 - exp(2*pi*i*k/n), 1), where i = sqrt(-1). - Paul Barry, Apr 15 2005 From Peter Luschny, Jun 09 2011: (Start) a(n) = Product_{k=1..n-1} (if(gcd(k,n) > 1, 2*Pi/Gamma(k/n)^2, 1). a(n) = Product_{k=1..n-1} (if(gcd(k,n) > 1, 2*sin(Pi*k/n), 1). (End) EXAMPLE 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). MAPLE A048671 := n -> ilcm(op(numtheory[divisors](n) minus {1, n})); seq(A048671(i), i=1..79); # Peter Luschny, Mar 21 2011 MATHEMATICA {1}~Join~Table[LCM @@ Most@ Divisors@ n, {n, 2, 79}] (* Michael De Vlieger, May 01 2016 *) PROG (PARI) a(n)=my(p=n); if(isprime(n)||(ispower(n, , &p)&&isprime(p)), n/p, n) \\ Charles R Greathouse IV, Jun 24 2011 (PARI) a(n)=my(p); if(isprimepower(n, &p), n/p, n) \\ Charles R Greathouse IV, May 02 2016 (Sage) def A048671(n) :     if n < 2 : return 1     else : D = divisors(n); D.pop()     return lcm(D) [A048671(i) for i in (1..79)] # Peter Luschny, Feb 03 2012 CROSSREFS Cf. A000142, A002944, A003418, A014963, A025527. Cf. A182936 gives the dual (greatest common divisor). Sequence in context: A277791 A243146 A349440 * A335023 A205959 A318503 Adjacent sequences:  A048668 A048669 A048670 * A048672 A048673 A048674 KEYWORD nonn,easy AUTHOR EXTENSIONS New definition based on a comment of David Wasserman by Peter Luschny, Mar 23 2011 STATUS approved

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Last modified January 19 22:12 EST 2022. Contains 350466 sequences. (Running on oeis4.)