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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). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

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))).

CROSSREFS

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

Cf. A025478 (least roots of perfect powers).

Cf. A157985.

Sequence in context: A334762 A305461 A043261 * A025479 A093640 A320538

Adjacent sequences:  A157983 A157984 A157985 * A157987 A157988 A157989

KEYWORD

sign

AUTHOR

Daniel Forgues, Mar 10 2009

STATUS

approved

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Last modified August 7 15:08 EDT 2020. Contains 336276 sequences. (Running on oeis4.)