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A157986
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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).
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3
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2, -2, -3, -2, -4, -2, -3, -5, 2, -2, -6, -4, 2, -2, -3, -7, 2, -2, 2, 3, 2, -5, -8, -2, 2, -3, -2, 2, 2, 2, -9, -2, 2, -4, 2, -6, 2, -2, 2, -2, 3, -10, 2, 2, 2, 4, -3, -2, 2, 2, 2, -2, 3, 2, -2, 2, 2, -11, 2, -7, -3, -2, 2, -4, 2, 2, 2, 3, -2, 2, 2, -5, 2, 2, 2, 3, -2, 2, -2, 2, 2, -12, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Daniel Forgues, Table of n, a(n) for n=1..10000
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FORMULA
| a(n) = {k}_n * (-1)^{Pi(m) - Pi(m-1)}
where {k}_n is the exponent of {m^k}_n (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) = {A025479(n)} * (-1)^{Pi(m) - Pi(m-1)}, with m = {A001597(n)}^{1/{A025479(n)}}.
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CROSSREFS
| Cf. A157985 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).
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: A073182 A049599 A043261 * A025479 A093640 A083903
Adjacent sequences: A157983 A157984 A157985 * A157987 A157988 A157989
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KEYWORD
| sign
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AUTHOR
| Daniel Forgues (squid(AT)zensearch.com), Mar 10 2009
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