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A050997 Fifth powers of primes. 68
32, 243, 3125, 16807, 161051, 371293, 1419857, 2476099, 6436343, 20511149, 28629151, 69343957, 115856201, 147008443, 229345007, 418195493, 714924299, 844596301, 1350125107, 1804229351, 2073071593, 3077056399, 3939040643, 5584059449, 8587340257, 10510100501 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers k such that A062799(k) = 5.
Let r(n) = (a(n)+1)/(a(n)-1)) if a(n) mod 4 = 3, (a(n)-1)/(a(n)+1)) otherwise; then Product_{n>=1} r(n) = (31/33) * (244/242) * (3124/3126) * (16808/16806) * ... = 246016/259875. - Dimitris Valianatos, Mar 09 2020
LINKS
Xavier Gourdon and Pascal Sebah, Some Constants from Number theory.
Eric Weisstein's World of Mathematics, MathWorld: Prime Power.
FORMULA
A056595(a(n)) = 3. - Reinhard Zumkeller, Aug 15 2011
Sum_{n>=1} 1/a(n) = P(5) = 0.0357550174... (A085965). - Amiram Eldar, Jul 27 2020
From Amiram Eldar, Jan 23 2021: (Start)
Product_{n>=1} (1 + 1/a(n)) = zeta(5)/zeta(10) (A157291).
Product_{n>=1} (1 - 1/a(n)) = 1/zeta(5) = 1/A013663. (End)
MATHEMATICA
Array[Prime[ # ]^5 &, 30] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)
PROG
(PARI) vector(66, n, prime(n)^5)
(Magma) [p^5: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 27 2014
(Haskell)
a050997 = (^ 5) . a000040
a050997_list = map (^ 5) a000040_list
-- Reinhard Zumkeller, Jun 03 2015
CROSSREFS
Cf. A258602.
Sequence in context: A153159 A113850 A046454 * A056572 A226098 A096960
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 22 14:33 EDT 2024. Contains 371905 sequences. (Running on oeis4.)