A235867 - OEIS

%I #31 Aug 21 2021 16:35:29

%S 77,119,133,187,217,253,287,301,319,323,341,391,399,403,407,413,437,

%T 469,517,551,553,559,583,589,623,651,667,707,713,731,737,749,779,781,

%U 803,817,851,869,871,889,893,899,903,913,917,935,943,959,969,1001,1003

%N G-cyclic numbers k such that A060968(k)^A060968(k) <> 1 (mod k) and A235863(k)^A235863(k) <> 1 (mod k).

%C For G-cyclic numbers see A235866.

%C All terms are composite. - _Bill McEachen_, Jul 16 2021

%H Bill McEachen, <a href="/A235867/b235867.txt">Table of n, a(n) for n = 1..10000</a>

%H Jose María Grau, A. M. Oller-Marcen, Manuel Rodriguez and D. Sadornil, <a href="http://arxiv.org/abs/1401.4708">Fermat test with Gaussian base and Gaussian pseudoprimes</a>, arXiv:1401.4708 [math.NT], 2014.

%o (PARI) genit(maxx)={arr2=List();arr=List();for(ptr=1,maxx,if( gcd(ptr,A060968(ptr))==1,listput(arr,ptr)));for(ptr=2,#arr,n=arr[ptr];a=A060968(n)^A060968(n);b=A235863(n)^A235863(n);if(a%n!=1&&b%n!=1,listput(arr2,n)));}

%o A060968(n)={my(f=factor(n)[,1]);q=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);return(q);} \\taken from that sequence

%o A235863(n)={my(f=factor(n));q=lcm(vector(#f~,i,my([p,e]=f[i,]);if(p==2,2^max(e-2,min(e,2)),p^(e-1)*if(p%4==1,p-1,p+1))));return (q);} \\taken from that sequence

%o \\ _Bill McEachen_, Jul 16 2021

%Y Cf. A235866, A060968, A235863.

%K nonn

%O 1,1

%A _José María Grau Ribas_, Feb 22 2014