Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I M2834 #18 Feb 17 2020 11:58:33
%S 3,10,21,55,78,136,171,253,406,465,666,820,903,1081,1378,1711,1830,
%T 2211,2485,2628,3081,3403,3916,4656,5050
%N Coefficients of period polynomials.
%C 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 D. H. and Emma Lehmer, Cyclotomy for nonsquarefree moduli, pp. 276-300 of Analytic Number Theory (Philadelphia 1980), Lect. Notes Math. 899 (1981).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 243.
%H Sean A. Irvine, <a href="/A006308/a006308_2.txt">The polynomials f(p,x) for primes p=3..101</a>
%F 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 Cf. A008837. [From _R. J. Mathar_, Oct 28 2008]
%K nonn
%O 2,1
%A _N. J. A. Sloane_.
%E More terms and offset corrected by _Sean A. Irvine_, Mar 07 2017