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A125131
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Product 1-p, where p ranges over the prime factors of n with multiplicity.
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0
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1, -1, -2, 1, -4, 2, -6, -1, 4, 4, -10, -2, -12, 6, 8, 1, -16, -4, -18, -4, 12, 10, -22, 2, 16, 12, -8, -6, -28, -8, -30, -1, 20, 16, 24, 4, -36, 18, 24, 4, -40, -12, -42, -10, -16, 22, -46, -2, 36, -16, 32, -12, -52, 8, 40, 6, 36, 28, -58, 8, -60, 30, -24, 1, 48, -20, -66, -16, 44, -24, -70, -4, -72, 36, -32
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OFFSET
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1,3
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COMMENTS
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f(1), where f is the monic polynomial whose zeros are the prime factors of n with multiplicity.
a(p) = 1-p for any prime number p.
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LINKS
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Table of n, a(n) for n=1..75.
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FORMULA
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Completely multiplicative with a(p) = 1-p. - Franklin T. Adams-Watters, Jan 17 2007
a(n) = f(1), where f(x)=(x-p_1)(x-p_2)...(x-p_m), where { p_1,p_2,...p_m } are the prime factors of n with multiplicity.
a(n) = A003958(n) * A008836(n).
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EXAMPLE
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a(120) = -8 because the prime factorization of 120 is 2*2*2*3*5, so f(x)=(x-2)(x-2)(x-2)(x-3)(x-5) and f(1)=(-1)*(-1)*(-1)*(-2)*(-4)= -8.
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MATHEMATICA
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f[n_] := Times @@ (-Flatten[Table[ #1, {#2}] & @@@ FactorInteger@n] + 1); Array[g, 80] (* Robert G. Wilson v, Jan 10 2007 *)
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PROG
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f=polyroot(factor(x)); f(1)
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CROSSREFS
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Cf. A003958, A008836.
Sequence in context: A046791 A187203 A187202 * A003958 A082729 A175542
Adjacent sequences: A125128 A125129 A125130 * A125132 A125133 A125134
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KEYWORD
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easy,sign,mult
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AUTHOR
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Mitch Cervinka (puritan(AT)toast.net), Jan 10 2007
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EXTENSIONS
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Edited by Franklin T. Adams-Watters, Jan 17 2007
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STATUS
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approved
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