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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved