A235867 G-cyclic numbers k such that A060968(k)^A060968(k) <> 1 (mod k) and A235863(k)^A235863(k) <> 1 (mod k).

77, 119, 133, 187, 217, 253, 287, 301, 319, 323, 341, 391, 399, 403, 407, 413, 437, 469, 517, 551, 553, 559, 583, 589, 623, 651, 667, 707, 713, 731, 737, 749, 779, 781, 803, 817, 851, 869, 871, 889, 893, 899, 903, 913, 917, 935, 943, 959, 969, 1001, 1003

Offset: 1

Author

José María Grau Ribas, Feb 22 2014

Keywords

• nonn

Comments

For G-cyclic numbers see A235866.

All terms are composite. - Bill McEachen, Jul 16 2021

Links

• Bill McEachen, Table of n, a(n) for n = 1..10000
• Jose María Grau, A. M. Oller-Marcen, Manuel Rodriguez and D. Sadornil, Fermat test with Gaussian base and Gaussian pseudoprimes, arXiv:1401.4708 [math.NT], 2014.

Crossrefs

Cf. A235866, A060968, A235863.

Programs

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)));}
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
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
\\ Bill McEachen, Jul 16 2021