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 A050997 Fifth powers of primes. 65
 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. Solutions of the equation n' = 5*n^(4/5), where n' is the arithmetic derivative of n. - Paolo P. Lava, Oct 31 2012 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 T. D. Noe, Table of n, a(n) for n = 1..1000 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. A000040, A001248, A030078, A030514, A085965, A131992, A131993, A013663, A157291. Cf. A258602. Sequence in context: A153159 A113850 A046454 * A056572 A226098 A096960 Adjacent sequences: A050994 A050995 A050996 * A050998 A050999 A051000 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified March 31 16:08 EDT 2023. Contains 361668 sequences. (Running on oeis4.)