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A050997 Fifth powers of primes. 62
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.

Index to sequences related to prime signature

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

Eric W. Weisstein

STATUS

approved

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Last modified September 24 19:27 EDT 2021. Contains 347651 sequences. (Running on oeis4.)