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).

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

Offset: 1

Author

Daniel Forgues, Mar 10 2009

Keywords

• sign

Links

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

Crossrefs

Cf. A001597 (perfect powers), A025479 (largest exponents of perfect powers).

Cf. A025478 (least roots of perfect powers).

Cf. A157985.

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))).