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A179665 a(n) = prime(n)^9. 20
512, 19683, 1953125, 40353607, 2357947691, 10604499373, 118587876497, 322687697779, 1801152661463, 14507145975869, 26439622160671, 129961739795077, 327381934393961, 502592611936843, 1119130473102767 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Solutions of the equation n' = 9*n^(8/9), where n' is the arithmetic derivative of n. - Paolo P. Lava, Oct 31 2012

Product_{n >= 2, m_n = (a(n) mod 4) - 2} ((a(n) + 1) / (a(n) - 1))^m_n = 209865342976 / 209844223875. - Dimitris Valianatos, May 13 2020

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

X. Gourdon and P. Sebah, Some Constants from Number theory

Will Nicholes, Prime Signatures

FORMULA

a(n) = A000040(n)^9 = A001017(A000040(n)). - Wesley Ivan Hurt, Mar 27 2014

Sum_{n>=1} 1/a(n) = P(9) = 0.0020044675... (A085969). - Amiram Eldar, Jul 27 2020

EXAMPLE

a(1) = 512 since the ninth power of the first prime is 2^9 = 512. - Wesley Ivan Hurt, Mar 27 2014

MAPLE

A179665:=n->ithprime(n)^9; seq(A179665(n), n=1..30); # Wesley Ivan Hurt, Mar 27 2014

MATHEMATICA

Array[Prime[ # ]^9&, 30]

PROG

(PARI) a(n)=prime(n)^9 \\ Charles R Greathouse IV, Jul 20 2011

(MAGMA) [p^9: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 27 2014

CROSSREFS

Cf. A006881, A007304, A065036, A085969, A085986, A085987, A178739, A179642, A179643, A179644, A179646, A179664.

Cf. A001248, A030078, A030514, A050997, A030516, A092759, A179645.

Sequence in context: A017682 A001017 A050756 * A056586 A096962 A231308

Adjacent sequences:  A179662 A179663 A179664 * A179666 A179667 A179668

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jul 23 2010

STATUS

approved

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Last modified October 24 04:47 EDT 2020. Contains 337975 sequences. (Running on oeis4.)