A182221 Composite numbers in A182140 but not in A071700.

255, 385, 34561, 65535, 147455, 195841, 1034881, 4070401, 4746241, 5040001, 16675201, 22704001, 36067201, 47013121, 83623935, 136967041, 168720001, 271878145, 549141119, 613092481, 836567041, 1039779841, 1049759999, 1548072961, 2556902401, 2646067201

Offset: 1

Author

José María Grau Ribas, Apr 19 2012

Keywords

• nonn

Comments

A182140 includes the prime numbers and A071700.

Links

• J. M. Grau, A. M. Oller-Marcen, M. Rodríguez, D. Sadornil, Fermat test with gaussian base and Gaussian pseudoprimes, arXiv preprint arXiv:1401.4708 [math.NT], 2014.

Crossrefs

Cf. A182140, A071700, A060968, A201629.

Programs

Mathematica

fa=FactorInteger;isA071700[n_]:=Length@fa[n]==2&&fa[n][[1,2]]==fa[n][[2,2]]==1&&Mod[Sqrt[n+1],4]==0; A060968[p_, s_] := Which[Mod[p, 4] == 1, p^(s-1)*(p-1), Mod[p, 4]==3, p^(s-1)*(p+1), s==1, 2, True, 2^(s+1)]; A060968[1]=1; A060968[n_] := Product[A060968[fa[n][[i, 1]], fa[n][[i, 2]]], {i, Length[fa[n]]}]; A201629[n_]:=Which[Mod[n, 4]==1, (n-1), Mod[n, 4]==3, (n+1), True, n];
Select[Range[10000], !isA071700[#]&&!PrimeQ[#]&&A060968[#]==A201629[#]&]

PARI

isA071700(n)=my(k=sqrtint(n\16)); n==16*k^2+32*k+15 && isprime(4*k+3) && isprime(4*k+5)
is(n)=if(isprime(n),return(0)); my(f=factor(n)[, 1]); n*prod(i=if(n%2, 1, 2), #f, if(f[i]%4==1, 1-1/f[i], 1+1/f[i]))*if(n%4, 1, 2)==if(n%2,(n+1)\4*4,n) && !isA071700(n) \\ Charles R Greathouse IV, Jul 03 2013

Extensions

a(15)-a(23) from Charles R Greathouse IV, Jul 03 2013

a(24)-a(26) from Charles R Greathouse IV, Jul 05 2013