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A020500
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Cyclotomic polynomials at x=1.
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20
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0, 2, 3, 2, 5, 1, 7, 2, 3, 1, 11, 1, 13, 1, 1, 2, 17, 1, 19, 1, 1, 1, 23, 1, 5, 1, 3, 1, 29, 1, 31, 2, 1, 1, 1, 1, 37, 1, 1, 1, 41, 1, 43, 1, 1, 1, 47, 1, 7, 1, 1, 1, 53, 1, 1, 1, 1, 1, 59, 1, 61, 1, 1, 2, 1, 1, 67, 1, 1, 1, 71, 1, 73, 1, 1, 1, 1, 1, 79, 1, 3
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OFFSET
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1,2
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COMMENTS
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Also the greatest common divisor of the prime factors of n. - Peter Luschny, Mar 22 2011
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LINKS
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FORMULA
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a(1) = 0; for n > 1, a(n) = gcd(lpf(n),gpf(n)), by Gallot's theorem 1.4. - Thomas Ordowski, May 04 2013
For n > 2, a(n) = lcm(1,2,...,n)/lcm(1,...,n-1). - Thomas Ordowski, Nov 01 2013
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MAPLE
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with(numtheory, cyclotomic); f := n->subs(x=1, cyclotomic(n, x)); seq(f(i), i=0..64);
A020500 := n -> igcd(op(numtheory[factorset](n))):
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MATHEMATICA
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Join[{0}, Table[GCD@@FactorInteger[n][[All, 1]], {n, 2, 80}]] (* Harvey P. Dale, Jul 18 2019 *)
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PROG
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(PARI) a(n) = if (n==1, 0, if (isprimepower(n, &p), p, 1)); \\ Michel Marcus, Nov 23 2016
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CROSSREFS
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Apart from initial zero, same as A014963.
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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