cp's OEIS Frontend

A182221 Composite numbers in A182140 but not in A071700.

%I A182221 #39 May 01 2020 16:20:05
%S A182221 255,385,34561,65535,147455,195841,1034881,4070401,4746241,5040001,
%T A182221 16675201,22704001,36067201,47013121,83623935,136967041,168720001,
%U A182221 271878145,549141119,613092481,836567041,1039779841,1049759999,1548072961,2556902401,2646067201
%N A182221 Composite numbers in A182140 but not in A071700.
%C A182221 A182140 includes the prime numbers and A071700.
%H A182221 J. M. Grau, A. M. Oller-Marcen, M. Rodríguez, D. Sadornil, <a href="http://arxiv.org/abs/1401.4708">Fermat test with gaussian base and Gaussian pseudoprimes</a>, arXiv preprint arXiv:1401.4708 [math.NT], 2014.
%t A182221 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];
%t A182221 Select[Range[10000], !isA071700[#]&&!PrimeQ[#]&&A060968[#]==A201629[#]&]
%o A182221 (PARI) isA071700(n)=my(k=sqrtint(n\16)); n==16*k^2+32*k+15 && isprime(4*k+3) && isprime(4*k+5)
%o A182221 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
%Y A182221 Cf. A182140, A071700, A060968, A201629.
%K A182221 nonn
%O A182221 1,1
%A A182221 _José María Grau Ribas_, Apr 19 2012
%E A182221 a(15)-a(23) from _Charles R Greathouse IV_, Jul 03 2013
%E A182221 a(24)-a(26) from _Charles R Greathouse IV_, Jul 05 2013