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A179645
a(n) = prime(n)^8.
26
256, 6561, 390625, 5764801, 214358881, 815730721, 6975757441, 16983563041, 78310985281, 500246412961, 852891037441, 3512479453921, 7984925229121, 11688200277601, 23811286661761, 62259690411361, 146830437604321
OFFSET
1,1
FORMULA
a(n) = A000040(n)^8 = A001016(A000040(n)). - Wesley Ivan Hurt, Mar 27 2014
Sum_{n>=1} 1/a(n) = P(8) = 0.0040614053... (A085968). - Amiram Eldar, Jul 27 2020
From Amiram Eldar, Jan 24 2021: (Start)
Product_{n>=1} (1 + 1/a(n)) = zeta(8)/zeta(16) = 34459425/(3617*Pi^8) = A013666/A013674.
Product_{n>=1} (1 - 1/a(n)) = 1/zeta(8) = 9450/Pi^8 = 1/A013666. (End)
EXAMPLE
a(1) = 256 since the eighth power of the first prime is 2^7 = 256. - Wesley Ivan Hurt, Mar 27 2014
MAPLE
A179645:=n->ithprime(n)^8; seq(A179645(n), n=1..40); # Wesley Ivan Hurt, Mar 27 2014
MATHEMATICA
Array[Prime[ # ]^8&, 40]
PROG
(PARI) a(n)=prime(n)^8 \\ Charles R Greathouse IV, Jul 20 2011
(Magma) [p^8: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 27 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved