1,2

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

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)}}.

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 this_sequence A001597 A072777 A076292

Adjacent sequences: A157982 A157983 A157984 this_sequence A157986 A157987 A157988

sign

Daniel Forgues (squid(AT)zensearch.com), Mar 10 2009