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A217863
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a(n) = phi(lcm(1,2,3,...,n)), where phi is Euler's totient function.
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4
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1, 1, 2, 4, 16, 16, 96, 192, 576, 576, 5760, 5760, 69120, 69120, 69120, 138240, 2211840, 2211840, 39813120, 39813120, 39813120, 39813120, 875888640, 875888640, 4379443200, 4379443200, 13138329600, 13138329600, 367873228800, 367873228800, 11036196864000
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OFFSET
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1,3
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COMMENTS
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This is a composition f(g(x)). g(x) = lcm(1...x) and f(x) = phi(x), Euler's totient function. The sequence generated is the number of prime congruence classes (prime spokes) for wheel factorization in mod g(x).
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LINKS
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FORMULA
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a(n) = Product_{k = 1..n} A072211(k).
With p denoting a prime, a(n) = ( Product_{p <= n} (p - 1) ) * ( Product_{p^2 <= n} p ) * ( Product_{p^3 <= n} p ) * ... . For example, a(16) = ((2-1)*(3-1)*(5-1)*(7-1)*(11-1)*(13-1)) * (2*3) * 2 * 2 = 138240. (End)
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MAPLE
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with(numtheory): a:=n->phi(lcm(seq(m, m=1..n))): seq(a(n), n=1..40); # Muniru A Asiru, Feb 20 2019
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MATHEMATICA
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EulerPhi[Table[LCM @@ Range[n], {n, 35}]] (* T. D. Noe, Oct 16 2012 *)
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PROG
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(Haskell)
(PARI) a(n) = eulerphi(lcm(vector(n, k, k))); \\ Michel Marcus, Aug 25 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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