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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
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: A358040 A305461 A043261 * A025479 A079243 A093640
KEYWORD
sign
AUTHOR
Daniel Forgues, Mar 10 2009
STATUS
approved

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Last modified July 23 21:46 EDT 2024. Contains 374575 sequences. (Running on oeis4.)