1,1

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

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)}}.

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 this_sequence A025479 A093640 A083903

Adjacent sequences: A157983 A157984 A157985 this_sequence A157987 A157988 A157989

sign

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