0,60

M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.

J.-P. Serre, On a theorem of Jordan, Bull. Amer. Math. Soc., 40 (No. 4, 2003), 429-440, see p. 434.

A. Granville and G. Martin, Prime number races

Expansion of eta(q)*eta(q^23) in powers of q.

Euler transform of period 23 sequence [ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, ...]. - Michael Somos, May 02 2005

G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=-v^3 + 2uvw + 2uw^2 + u^2w. - Michael Somos, May 02 2005

G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)=u1^2u3*6 +2u1u2u3u6 -2u1u6^3 +2u2^2u3u6 -u2u3^3. - Michael Somos, May 02 2005

a(n) is multiplicative and a(23^e) = 1. Let y = number of zeros of x^3-x-1 modulo p, then a(p^e) = (1+(-1)^e)/2 if y=1, a(p^e) = e+1 if y=3, a(p^e) = (e-1)%3-1 if y=0. - Michael Somos Oct 19 2005

a(8n+4)=a(23n+5)=a(23n+7)=a(23n+10)=a(23n+11)=a(23n+14)=a(23n+15)=a(23n+19)=a(23n+20)=a(23n+21)=a(23n+22)=0. - Michael Somos Oct 19 2005

a(n) is multiplicative and a(23^e) = 1. Let y = number of roots of x^3-x-1 modulo p, then a(p^e) = (1+(-1)^e)/2 if y=1, a(p^e) = e+1 if y=3, a(p^e) = (e-1)%3-1 if y=0. - Michael Somos Oct 19 2005

q -q^2 -q^3 +q^6 +q^8 -q^13 -q^16 +q^23 -q^24 +q^25 +...

(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x+A)*eta(x^23+A), n))} /* Michael Somos May 02 2005 */

(PARI) {a(n)=local(A, p, e, y); if(n<1, 0, A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==23, 1, y=sum(x=1, p-1, (x^3-x-1)%p==0); if(y==1, 1-e%2, if(y, e+1, (e-1)%3-1))))))} /* Michael Somos Oct 19 2005 */

Sequence in context: A116376 A165766 A102082 this_sequence A005089 A119395 A087476

Adjacent sequences: A030196 A030197 A030198 this_sequence A030200 A030201 A030202

sign,mult

N. J. A. Sloane (njas(AT)research.att.com).