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

1,1

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.

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[#]] &]

Prog

(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

Crossrefs

Cf. A235863, A201629.

Sequence in context: A099309 A327929 A327864 * A311086 A311087 A311088

Adjacent sequences: A235862 A235863 A235864 * A235866 A235867 A235868

Keyword

nonn

Author

José María Grau Ribas, Jan 16 2014

Extensions

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

Status

approved