A109255 a(n) = (p^2 - 1) / 12, where p is the n-th prime of the form 4*k+1.

2, 14, 24, 70, 114, 140, 234, 310, 444, 660, 784, 850, 990, 1064, 1564, 1850, 2054, 2494, 2730, 3104, 3234, 4370, 4524, 4840, 5504, 6030, 6394, 6580, 7154, 8164, 8374, 9464, 10150, 10384, 11594, 12610, 13134, 13400, 13940, 14770, 15624, 16800, 17404

Offset

1,1

References

G. Pólya and G. Szegő, Problems and Theorems in Analysis II (Springer 1924, reprinted 1972), Part Eight, Chap. 1, Sect. 2, Problem 20.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = (A002144(n)^2 - 1) / 12.

a(n) = Sum_{k=1..(p-1)/4} floor(sqrt(k*p)), where p = primes of the form 4*n+1.

Mathematica

Map[(#^2 - 1)/12 &, Select[4 Range[120] + 1, PrimeQ]] (* Michael De Vlieger, Dec 27 2019 *)

Prog

(Magma) [(p^2 - 1) / 12: p in PrimesUpTo(500)| p mod 4 eq 1]; // Marius A. Burtea, Dec 29 2019

Crossrefs

Cf. A002144.

Sequence in context: A036433 A172048 A226334 * A285990 A174594 A051222

Adjacent sequences: A109252 A109253 A109254 * A109256 A109257 A109258

Keyword

nonn

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved