OFFSET
1,1
COMMENTS
Apart from the first term, the same as A117762. - R. J. Mathar, Jun 14 2008
Except the first term, a(n) is the area of the integer-sided isosceles triangle ABC with AB=AC such that the altitude AH is of prime(n) length.
The couples (a(n), altitude) are (12,3), (60,5), (168,7), (660,11), (1092,13), ... and the sequence of the ratio a(n)/prime(n) is {4, 12, 24, 60, 84, 144, 180, ...} - see A084921. - Michel Lagneau, Oct 23 2013
a(n) is also equal to the number of reducible quadratic polynomials in the field of size prime(n). - James East, Apr 26 2024
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
MATHEMATICA
Table[(Prime[n] + 1) Prime[n](Prime[n] - 1)/2, {n, 1, 100}]
PROG
(PARI) forprime(p=2, 1e3, print1(3*binomial(p+1, 3)", ")) \\ Charles R Greathouse IV, Jun 16 2011
(Magma) [(NthPrime(n)+1)*NthPrime(n)*(NthPrime(n)-1)/2: n in [1..40]]; // Vincenzo Librandi, Apr 09 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Feb 06 2007
STATUS
approved