

A171555


Numbers of the form prime(n)*(prime(n)1)/4.


7



5, 39, 68, 203, 333, 410, 689, 915, 1314, 1958, 2328, 2525, 2943, 3164, 4658, 5513, 6123, 7439, 8145, 9264, 9653, 13053, 13514, 14460, 16448, 18023, 19113, 19670, 21389, 24414, 25043, 28308, 30363, 31064, 34689, 37733, 39303, 40100, 41718, 44205, 46764, 50288
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OFFSET

1,1


COMMENTS

The halfs of even numbers of p(p1)/2 for p prime.
Sum of the quadratic residues of primes of the form 4k + 1. For example, a(3)=68 because 17 is the 3rd prime of the form 4k + 1 and the quadratic residues of 17 are 1, 4, 9, 16, 8, 2, 15, 13 which sum to 68. This sum is also the sum of the quadratic nonresidues. Cf. A230077.  Geoffrey Critzer, May 07 2015


REFERENCES

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see Exercise 2.21 p. 110.


LINKS



MATHEMATICA

Table[Table[Mod[a^2, p], {a, 1, (p  1)/2}] // Total, {p,
Select[Prime[Range[100]], Mod[#, 4] == 1 &]}] (* Geoffrey Critzer, May 07 2015 *)
Select[(# (#1))/4&/@Prime[Range[100]], IntegerQ] (* Harvey P. Dale, Dec 24 2022 *)


PROG

(PARI) lista(nn) = forprime(p=2, nn, if ((p % 4)==1, print1(p*(p1)/4, ", "))); \\ Michel Marcus, Mar 23 2016


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

Corrected (16448 inserted, 25043 inserted) by R. J. Mathar, May 22 2010


STATUS

approved



