A131991 a(n) = 1 + prime(n) + prime(n)^2 + prime(n)^3.

15, 40, 156, 400, 1464, 2380, 5220, 7240, 12720, 25260, 30784, 52060, 70644, 81400, 106080, 151740, 208920, 230764, 305320, 363024, 394420, 499360, 578760, 712980, 922180, 1040604, 1103440, 1236600, 1307020, 1455780, 2064640, 2265384

Offset: 1

Author

Reinhard Zumkeller, Aug 06 2007

Keywords

• nonn
• easy

Comments

Number of points and lines for the prime(n)-Cremona-Richmond configuration. - Carlos Segovia Gonzalez, Jul 30 2020

Examples

			a(4)=400 because the 4th prime is 7, 7^3=343, 7^2=49, and 343+49+7+1=400.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• C. Segovia and M. Winklmeier, Calculating the dimension of the universal embedding of the symplectic dual polar space using languages, arXiv:1312.4315 [math.CO], 2013-2019.
• C. Segovia and M. Winklmeier, Calculating the dimension of the universal embedding of the symplectic dual polar space using languages, The Elec. Jour. of Comb. 27(4) (2020), P4.39.

Crossrefs

Cf. A030078, A008864, A131992, A131993.

Cf. A000040, A000203. - Zak Seidov, Feb 13 2016

Programs

Magma

[1+NthPrime(n)+NthPrime(n)^2+NthPrime(n)^3: n in [1..40]]; // Vincenzo Librandi, Dec 27 2010

Maple

A131991:= n -> map (p -> p^(3)+p^(2)+p+1, ithprime(n)):
seq (A131991(n), n=1..32); # Jani Melik, Jan 25 2011

Mathematica

#^3 + #^2 + # + 1 &/@Prime[Range[100]] (* Vincenzo Librandi, Mar 20 2014 *)

Formula

a(n) = 1 + A060800(n)*A000040(n).

a(n) = (A030514(n) - 1)/A006093(n).

a(n) = A000203(A000040(n)^3). - Zak Seidov, Feb 13 2016