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A050997
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Fifth powers of primes.
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65
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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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.
Index to sequences related to prime signature
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FORMULA
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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)
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MATHEMATICA
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Array[Prime[ # ]^5 &, 30] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein
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STATUS
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approved
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