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A050997
Fifth powers of primes.
71
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
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
KEYWORD
nonn,easy
STATUS
approved