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A157985
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Perfect powers (m^k where m is an integer and k >= 2) multiplied by -1 when m is prime for largest k (m^k thus a prime power).
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3
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1, -4, -8, -9, -16, -25, -27, -32, 36, -49, -64, -81, 100, -121, -125, -128, 144, -169, 196, 216, 225, -243, -256, -289, 324, -343, -361, 400, 441, 484, -512, -529, 576, -625, 676, -729, 784, -841, 900, -961, 1000, -1024, 1089, 1156, 1225, 1296, -1331
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OFFSET
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1,2
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COMMENTS
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The rather strange phrase "largest k" in the definition refers to the fact that there can be several ways to write a number in the form m^k. - N. J. A. Sloane, Jan 01 2019
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LINKS
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FORMULA
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a(n) = {m^k}_n * (-1)^(Pi(m) - Pi(m-1)) where {m^k}_n is the n-th perfect power with positive integer base m corresponding to largest integer exponent k and Pi(m) is the prime counting function evaluated at m.
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CROSSREFS
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Cf. A001597 (perfect powers), A025479 (largest exponents of perfect powers.
Cf. A025478 (least roots of perfect powers).
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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