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

1,1

Comments

A182140 includes the prime numbers and A071700.

Links

Table of n, a(n) for n=1..26.

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.

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[#]&]

Prog

(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

Crossrefs

Cf. A182140, A071700, A060968, A201629.

Sequence in context: A306223 A023690 A101745 * A053339 A031197 A043348

Adjacent sequences: A182218 A182219 A182220 * A182222 A182223 A182224

Keyword

nonn

Author

José María Grau Ribas, Apr 19 2012

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

Status

approved