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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). 3
1, -4, -8, -9, -16, -25, -27, -32, 36, -49, -64, -81, 100, -121, -125, -128, 144, -169, 196, 216, 225, -243, -256, -289, 324, -343, -361, 400, 441, 484, -512, -529, 576, -625, 676, -729, 784, -841, 900, -961, 1000, -1024, 1089, 1156, 1225, 1296, -1331 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The rather strange phrase "largest k" in the definition refers to the fact that there can be several ways to write a number in the form m^k. - N. J. A. Sloane, Jan 01 2019

LINKS

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

FORMULA

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)).

CROSSREFS

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

Cf. A025478 (least roots of perfect powers).

Cf. A157986.

Sequence in context: A080366 A001694 A317102 * A001597 A072777 A076292

Adjacent sequences:  A157982 A157983 A157984 * A157986 A157987 A157988

KEYWORD

sign

AUTHOR

Daniel Forgues, Mar 10 2009

STATUS

approved

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Last modified August 4 19:07 EDT 2020. Contains 336202 sequences. (Running on oeis4.)