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, -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

Offset: 1

Author

Daniel Forgues, Mar 10 2009, Mar 14 2009

Keywords

• sign

Links

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

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).

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)}}.