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A081115 (p^2 - 1)/12 where p > 3 runs through the primes. 3
2, 4, 10, 14, 24, 30, 44, 70, 80, 114, 140, 154, 184, 234, 290, 310, 374, 420, 444, 520, 574, 660, 784, 850, 884, 954, 990, 1064, 1344, 1430, 1564, 1610, 1850, 1900, 2054, 2214, 2324, 2494, 2670, 2730, 3040, 3104, 3234, 3300, 3710, 4144, 4294, 4370, 4524 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

If p=4k+1, (p^2 - 1)/12 = Sum_{i=1..k} floor(sqrt(i*k)) (see links). - R. J. Mathar, Jul 07 2006

For n=1 and 2, the corresponding primes being 2 and 3, and a(n) is a fraction, not entered here. - Michel Marcus, Nov 11 2013

For prime p > 3, (p^2 - 1)/12 = (1/p)*Sum_{k=0..floor(p/2)} (p - k)*k. - Joseph Wheat, Feb 03 2018

LINKS

Muniru A Asiru, Table of n, a(n) for n = 3..5000

Hojoo Lee, Problems in Elementary Number Theory, p. 14, problem 10.

George PĆ³lya and Gabor Szego, Problems and Theorems in Analysis II, p. 113, problem 20.

S. A. Shirali, A family portrait of primes -- a case study in discrimination, Math. Mag.. Vol. 70, No. 4 (Oct. 1997), pp. 263-272.

FORMULA

a(n) = j*(j+1)/3 where A000040(n)=2*j+1. - R. J. Mathar, Jul 07 2006

a(n) = (A001248(n) - 1)/12. - Vicente Izquierdo Gomez, May 25 2013

a(n) = 2*A024702(n). - R. J. Mathar, Jan 09 2017

MAPLE

seq((ithprime(p)^2-1)/12, p=3..20); # Muniru A Asiru, Feb 04 2018

MATHEMATICA

(Prime[Range[3, 51]]^2 - 1)/12 (* Giovanni Resta, May 25 2013 *)

PROG

(PARI) a(n) = p = prime(n); (p^2-1)/12; \\ Michel Marcus, Nov 11 2013

(GAP) List(Filtered([5..20], IsPrime), p->(p^2-1)/12); # Muniru A Asiru, Feb 04 2018

CROSSREFS

Sequence in context: A139480 A227388 A152749 * A053417 A082230 A236547

Adjacent sequences:  A081112 A081113 A081114 * A081116 A081117 A081118

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Apr 16 2003

EXTENSIONS

Offset set to 3 and edited by Michel Marcus, Nov 11 2013

STATUS

approved

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Last modified December 19 10:10 EST 2018. Contains 318246 sequences. (Running on oeis4.)