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 A189914 a(n) is 2^phi(n) times the least common multiple of the proper divisors of n. 1
 1, 2, 2, 4, 8, 16, 24, 64, 64, 192, 160, 1024, 192, 4096, 896, 3840, 2048, 65536, 1152, 262144, 5120, 86016, 22528, 4194304, 6144, 5242880, 106496, 2359296, 114688, 268435456, 7680, 1073741824, 1048576, 34603008, 2228224, 587202560, 147456, 68719476736, 9961472 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The sequence relates arithmetic properties of roots of unity in the complex plane with number theoretic properties of integers. This connection often appears as intriguing identities showing products of specific values of the sine function or the gamma function reducing to simple values (see for instance the first formula below). LINKS Charles R Greathouse IV, Table of n, a(n) for n = 0..3322 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], Sep 2009. Albert Nijenhuis, Short Gamma Products with Simple Values, The American Mathematical Monthly, Vol. 117, No. 8, Oct 2010, pp. 733-737. J. Sándor and L. Tóth, A remark on the gamma function, Elemente der Mathematik, 44 (1989), pp. 73-76, Birkhäuser. FORMULA Let R(n) = {k | gcd(n,k) = 1, k = 1..floor(n/2)} and b(n) = product_{R(n)} sin(Pi*k/n) then a(n) = n / b(n)^2 for n > 1. a(n) = A066781(n)*A048671(n). MAPLE A189914 := n -> 2^numtheory[phi](n)*ilcm(op(numtheory[divisors](n) minus {1, n})): seq(A189914(n), n=0..35); MATHEMATICA a[n_] := 2^EulerPhi[n] * LCM @@ Most[Divisors[n]]; a[0] = 1; a[1] = 2; Table[a[n], {n, 0, 38}] (* Jean-François Alcover, Jan 22 2014 *) PROG (PARI) a(n)=if(n, my(p=n); if(isprime(n)||(ispower(n, , &p)&&isprime(p)), n/p, n)<

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Last modified June 1 04:57 EDT 2020. Contains 334758 sequences. (Running on oeis4.)