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.
%I A006308 M2834 #22 Jul 08 2025 16:46:58
%S A006308 3,10,21,55,78,136,171,253,406,465,666,820,903,1081,1378,1711,1830,
%T A006308 2211,2485,2628,3081,3403,3916,4656,5050
%N A006308 Coefficients of period polynomials.
%C A006308 Conjecture: a(n) = A008837(n) = p*(p-1)/2 = Sum_{k=0..p-1} mod(k^3, p) where p = prime(n). - _Michael Somos_, Feb 17 2020
%D A006308 D. H. and Emma Lehmer, Cyclotomy for nonsquarefree moduli, pp. 276-300 of Analytic Number Theory (Philadelphia 1980), Lect. Notes Math. 899 (1981).
%D A006308 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A006308 J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 243.
%H A006308 Sean A. Irvine, <a href="/A006308/a006308_2.txt">The polynomials f(p,x) for primes p=3..101</a>
%F A006308 For an odd prime p, let g be a primitive root of p^2, q=g^p, and zeta=exp(2*pi*i/p^2). Define h(p,k) = Sum_{j=0..p-2} zeta^((q+k*p)*q^j) and a polynomial f(p,x) = Product_{k=0..p-1} (x-h(p,k)). Finally, a(n) = -[x^(p-2)] f(p,x) where p = A000040(n) is the n-th prime. - _Sean A. Irvine_, Mar 07 2017
%Y A006308 Cf. A008837. [From _R. J. Mathar_, Oct 28 2008]
%K A006308 nonn
%O A006308 2,1
%A A006308 _N. J. A. Sloane_
%E A006308 More terms and offset corrected by _Sean A. Irvine_, Mar 07 2017