OFFSET
1,1
COMMENTS
When prime(n) = m^2 + 1 is a Landau prime (A002496), a(n) + 1 = (m*prime(n))^2 + 1, the Gaussian norm of m*prime(n) + i in Z[i]. - Steven Lee Benjamin, Apr 23 2026
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)
FORMULA
a(n) = A000010(prime(n)^3). - R. J. Mathar, Oct 15 2017
Sum_{n>=1} 1/a(n) = A152441. - Amiram Eldar, Nov 09 2020
From Amiram Eldar, Nov 22 2022: (Start)
Product_{n>=1} (1 + 1/a(n)) = A065483.
Product_{n>=1} (1 - 1/a(n)) = A065414. (End)
a(n) = 2*A138416(n). - Antti Karttunen, Dec 14 2024
From Steven Lee Benjamin, Apr 23 2026: (Start)
a(n) = A078429(prime(n)^3) - 1.
a(n) = A100104(prime(n)) - 1. (End)
EXAMPLE
a(4) = 294 because the 4th prime number is 7, 7^2 = 49, 7-1 = 6 and 49 * 6 = 294.
MATHEMATICA
Table[Prime[n]^3-Prime[n]^2, {n, 1, 12}] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)
(* Alternative: *)
Table[p^3-p^2, {p, Prime[Range[40]]}] (* Harvey P. Dale, Jan 15 2015 *)
PROG
(Magma)[(p^3-p^2): p in PrimesUpTo(200)]; // Vincenzo Librandi, Dec 15 2010
(PARI) forprime(p=2, 1e3, print1(p^2*(p-1)", ")) \\ Charles R Greathouse IV, Jun 16 2011
(PARI) A135177(n) = eulerphi(prime(n)^3); \\ Antti Karttunen, Dec 14 2024
(PARI) A135177(n) = ((p->(p-1)*p*p)(prime(n))); \\ Antti Karttunen, Dec 14 2024
CROSSREFS
Column 4 of A379010.
KEYWORD
nonn,easy,changed
AUTHOR
Omar E. Pol, Nov 25 2007
STATUS
approved
