OFFSET
1,1
COMMENTS
These are the numbers p^6 with p prime. - Jorge Coveiro, Apr 13 2004
The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. - Omar E. Pol, May 06 2008
LINKS
FORMULA
A056595(a(n)) = 3. - Reinhard Zumkeller, Aug 15 2011
Sum_{n>=1} 1/a(n) = P(6) = 0.0170700868... (A085966). - Amiram Eldar, Jul 27 2020
From Amiram Eldar, Jan 23 2021: (Start)
Product_{n>=1} (1 + 1/a(n)) = zeta(6)/zeta(12) = 675675/(691*Pi^6) (A269404).
Product_{n>=1} (1 - 1/a(n)) = 1/zeta(6) = 945/Pi^6 = 1/A013664. (End)
MATHEMATICA
Array[Prime[ # ]^6&, 60] (* Vladimir Joseph Stephan Orlovsky, Dec 14 2009 *)
PROG
(Sage)
[p**6 for p in prime_range(100)]
# Zerinvary Lajos, May 16 2007
(PARI) for(n=1, 1e3, print1(prime(n)^6", ")); \\ Bruno Berselli, Jul 30 2011
(Magma) [NthPrime(n)^6: n in [1..400]]; // Bruno Berselli, Jul 30 2011
(Haskell)
a030516 = (^ 6) . a000040
a030516_list = map (^ 6) a000040_list
-- Reinhard Zumkeller, Jun 03 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved