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A127918
Half of product of three numbers: n-th prime, previous and following number.
9
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
1,1
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
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