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A157987 Smallest roots m of perfect powers (m^k where m is an integer and k >= 2) multiplied by -1 when m is prime (m^k thus a prime power). 1
1, -2, -2, -3, -2, -5, -3, -2, 6, -7, -2, -3, 10, -11, -5, -2, 12, -13, 14, 6, 15, -3, -2, -17, 18, -7, -19, 20, 21, 22, -2, -23, 24, -5, 26, -3, 28, -29, 30, -31, 10, -2, 33, 34, 35, 6, -11, -37, 38, 39, 40, -41, 12, 42, -43, 44, 45, -2, 46, -3, -13, -47, 48, -7, 50, 51, 52 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Daniel Forgues, Table of n, a(n) for n=1..10000

FORMULA

a(n) = {m}_n * (-1)^{Pi(m) - Pi(m-1)}

where {m}_n is the smallest root 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) = m * (-1)^{Pi(m) - Pi(m-1)}, with m = A025478(n) = {A001597(n)}^{1/{A025479(n)}}.

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. 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).

Sequence in context: A254269 A264662 A076403 * A025478 A084371 A025476

Adjacent sequences:  A157984 A157985 A157986 * A157988 A157989 A157990

KEYWORD

sign

AUTHOR

Daniel Forgues, Mar 10 2009, Mar 14 2009

STATUS

approved

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Last modified September 30 03:30 EDT 2020. Contains 337432 sequences. (Running on oeis4.)