cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A125614 (Sum of the squares of the quadratic residues of prime(n)) / prime(n).

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%I A125614 #14 Dec 19 2024 19:07:16
%S A125614 3,12,27,48,46,48,139,106,229,286,276,239,469,477,627,698,574,914,823,
%T A125614 1003,1350,1612,1713,1485,1721,2007,2172,2339,2500,3190,2977,3733,
%U A125614 3234,4155,4306,3688,5023,4848,5529,4791,6356,6517,5655,7051,7452,7964,8845
%N A125614 (Sum of the squares of the quadratic residues of prime(n)) / prime(n).
%C A125614 Always an integer for primes > 5.
%D A125614 D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 185.
%H A125614 Nick Hobson, <a href="/A125614/b125614.txt">Table of n, a(n) for n = 4..1003</a>
%F A125614 a(n) = A125613(n)/prime(n).
%e A125614 The quadratic residues of 7=prime(4) are 1, 2 and 4. Hence a(4) = (1^2 + 2^2 + 4^2)/7 = 3.
%t A125614 Table[Total[ResourceFunction["QuadraticResidues"][Prime[n]]^2/Prime[n]], {n,4, 50}] (* _James C. McMahon_, Dec 19 2024 *)
%o A125614 (PARI) vector(47, m, p=prime(m+3); t=1; for(i=2, (p-1)/2, t+=((i^2)%p)^2); t/p)
%Y A125614 Cf. A076409, A076410, A125613-A125618.
%K A125614 easy,nonn
%O A125614 4,1
%A A125614 _Nick Hobson_, Nov 30 2006