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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Daniel Forgues, Table of n, a(n) for n=1..10000
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FORMULA
| 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.
a(n) = {A001597(n)} * (-1)^{Pi(m) - Pi(m-1)}, with m = {A001597(n)}^{1/{A025479(n)}}.
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CROSSREFS
| Cf. A157986 Largest exponents of perfect powers (m^k where m is an integer and k >= 2) multiplied by -1 when base m is prime (m^k thus a prime power).
Cf. A001597 Perfect powers: m^k where m is an integer and k >= 2.
Cf. A025479 Largest exponents of perfect powers (A001597).
Cf. A025478 Least roots of perfect powers (A001597). [From Daniel Forgues (squid(AT)zensearch.com), Mar 14 2009]
Sequence in context: A158804 A080366 A001694 * A001597 A072777 A076292
Adjacent sequences: A157982 A157983 A157984 * A157986 A157987 A157988
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KEYWORD
| sign
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AUTHOR
| Daniel Forgues (squid(AT)zensearch.com), Mar 10 2009
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