A127918 Half of product of three numbers: n-th prime, previous and following number.

3, 12, 60, 168, 660, 1092, 2448, 3420, 6072, 12180, 14880, 25308, 34440, 39732, 51888, 74412, 102660, 113460, 150348, 178920, 194472, 246480, 285852, 352440, 456288, 515100, 546312, 612468, 647460, 721392, 1024128, 1123980, 1285608

Offset: 1

Author

Artur Jasinski, Feb 06 2007

Keywords

• nonn
• easy

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

Crossrefs

Cf. A036689, A034953, A127917, A127920.

Programs

Magma

[(NthPrime(n)+1)*NthPrime(n)*(NthPrime(n)-1)/2: n in [1..40]]; // Vincenzo Librandi, Apr 09 2017

Mathematica

Table[(Prime[n] + 1) Prime[n](Prime[n] - 1)/2, {n, 1, 100}]

PARI

forprime(p=2,1e3,print1(3*binomial(p+1,3)", ")) \\ Charles R Greathouse IV, Jun 16 2011