A235865 G-Carmichael numbers: Composite number such that A235863(n) divides A201629(n).

4, 8, 12, 15, 16, 20, 24, 32, 36, 40, 48, 56, 60, 64, 72, 80, 96, 100, 105, 108, 112, 120, 128, 132, 143, 144, 156, 160, 168, 180, 192, 200, 216, 224, 240, 255, 256, 264, 272, 280, 288, 300, 312, 320, 324, 336, 360, 380, 384, 385, 392, 396, 399, 400, 432

Offset: 1

Author

José María Grau Ribas, Jan 16 2014

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1038
• 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. A235863, A201629.

Programs

Mathematica

FU[n_] := Which[Mod[n, 4] == 3, n + 1, Mod[n, 4] == 1, n - 1, True, n]; fa = FactorInteger; lam[1] = 1; lam[p_,s_] := Which[Mod[p, 4] == 3, p^(s - 1) (p + 1), Mod[p, 4] == 1, p^(s - 1) (p - 1), s ≥ 5, 2^(s -2), s > 1, 4, s == 1, 2]; lam[n_] := {aux = 1; Do[aux = LCM[aux, lam[fa[n][[i, 1]], fa[n][[i, 2]]]], {i, 1, Length[fa[n]]}]; aux}[[1]];Select[1+Range[1000], ! PrimeQ[#] && IntegerQ[FU[#]/lam[#]] &]

PARI

ok(n)={my(f=factor(n), r=n-kronecker( -4, n)); for(i=1, #f~, my([p, e]=f[i, ]); my(t=if(p==2, 2^max(e-2, min(e, 2)), p^(e-1)*if(p%4==1, p-1, p+1))); if(r%t, return(0)) ); n>1 && !isprime(n)} \\ Andrew Howroyd, Aug 06 2018

Extensions

a(55) corrected by Andrew Howroyd, Aug 06 2018