A038791 An intermediate sequence for nonisomorphic circulant p^2-tournaments, indexed by odd primes p.

2, 4, 12, 104, 344, 4096, 14572, 190652, 9586984, 35791472, 1908874584, 27487790720, 104715393912, 1529755308212, 86607685141744, 4969489243995032, 19215358410149344, 1117984489315857512, 16865594581677305360, 65588423373189982912

Offset: 2

Author

N. J. A. Sloane, May 04 2000

Keywords

• nonn
• easy

Comments

Number of subsets of {1, ..., p} with product = 1 mod p, where p is the n-th prime. - Charles R Greathouse IV, Jun 06 2013

Also : Number of subsets of {1, ..., p} with product = -1 mod p, where p is the n-th prime. - Ridouane Oudra, Jul 08 2025

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 2..100
• M. Klin, V. A. Liskovets and R. Poeschel, Analytical enumeration of circulant graphs with prime-squared vertices, Sem. Lotharingien de Combin., B36d, 1996, 36 pages.

Crossrefs

Cf. A038787, A238446.

Programs

Mathematica

has[p_] := Module[{v, u}, v = Table[0, {p-1}]; v[[1]] = 1; For[n = 2, n <= p-1, n++, u = Table[0, {p-1}]; For[j = 1, j <= p-1, j++, u[[Mod[j*n, p]]] += v[[j]]]; v += u]; 2*v[[1]]];
a[n_] := has[Prime[n]];
Table[a[n], {n, 2, 21}] (* Jean-François Alcover, Aug 30 2019, after Charles R Greathouse IV *)

PARI

has(p)=my(v=vector(p-1),u); v[1]=1; for(n=2,p-1,u=vector(p-1); for(j=1,p-1, u[j*n%p]+=v[j]);v+=u); 2*v[1]
a(n)=has(prime(n)) \\ Charles R Greathouse IV, Jun 06 2013

Formula

a(p^2) = A038790(p^2) - A038789(p^2) + A038792(p^2).

a(n) = A238446(n) + 1. - Ridouane Oudra, Jul 08 2025

Extensions

More terms from Valery A. Liskovets, May 09 2001

a(12)-a(20) from Charles R Greathouse IV, Jun 06 2013