A038787 -id:A038787 - cp's OEIS frontend

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

N. J. A. Sloane, May 04 2000

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

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.

Cf. A038787, A238446.

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 *)

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

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

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

More terms from Valery A. Liskovets, May 09 2001

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

A038788 Non-Cayley-isomorphic circulant self-complementary directed p^2-graphs, indexed by odd primes p.

Original entry on oeis.org

1, 4, 4, 16, 64, 400, 900, 8836, 355216, 1201216, 53523856, 690217984, 2494003600, 33255899044, 1666350520384, 85680866908816, 320296595636224, 16939175556745744, 240937075998869056, 910964509740273664, 49676441991516395584, 719170624451273114176

Offset: 1

N. J. A. Sloane, May 04 2000

V. A. Liskovets and R. Poeschel, Non-Cayley-isomorphic self-complementary circulant graphs, J. Graph Th., 34, 2000, 128-141.

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.

Cf. A038785, A038787.

a(p^2) = A049309(p)^2.
a(p^2) = A054246(p^2) for p=4k-1.
a(p^2) = ( (1/(p-1)) * Sum_{r|p-1 and r even} phi(r) * 2^((p-1)/r) )^2. - Sean A. Irvine, Feb 14 2021

More terms from Valery A. Liskovets, May 09 2001

More terms and offset corrected by Sean A. Irvine, Feb 14 2021

A061848 An intermediate sequence for nonisomorphic circulant self-complementary undirected p^2-graphs, indexed by odd primes p.

Original entry on oeis.org

0, 2, 0, 0, 12, 38, 0, 0, 1172, 0, 14572, 52536, 0, 0, 2581112, 0, 35791472, 0, 0, 1908889156, 0, 0, 399822600756, 5864062716964, 22517998136936, 0, 0, 333599972407532, 1286742760265468, 0, 0, 4340410370789890656, 0, 255263053128088930472, 0

Offset: 3

Valery A. Liskovets, May 09 2001

nonn

a(p^2)=0 for p=4k-1

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.

Cf. A038787.

a(p^2)= A061847(p^2) - A061846(p^2) + A061849(p^2)

More terms from Sean A. Irvine, Mar 09 2023

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

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A038788 Non-Cayley-isomorphic circulant self-complementary directed p^2-graphs, indexed by odd primes p.

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A061848 An intermediate sequence for nonisomorphic circulant self-complementary undirected p^2-graphs, indexed by odd primes p.

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