A235864 - OEIS

%I #26 Nov 24 2023 08:10:27

%S 15,143,255,385,3599,5183,11663,32399,34561,36863,51983,57599,65535,

%T 97343,121103,147455,176399,186623,195841,359999,435599,685583,

%U 1034881,1040399,1065023,1192463,1327103,1742399,2039183,2108303,2214143,2585663,2624399,2782223,3196943

%N G-Lehmer numbers: Composite numbers k such that A060968(k) divides A201629(k).

%H Amiram Eldar, <a href="/A235864/b235864.txt">Table of n, a(n) for n = 1..1000</a>

%H José María Grau, Antonio M. Oller-Marcén, Manuel Rodríguez, and Daniel Sadornil, <a href="https://doi.org/10.1007/s10587-015-0221-2">Fermat test with Gaussian base and Gaussian pseudoprimes</a>, Czechoslovak Mathematical Journal, Vol. 65 (2015), pp. 969-982; <a href="https://arxiv.org/abs/1401.4708">arXiv preprint</a>, arXiv:1401.4708 [math.NT], 2014.

%t fa=FactorInteger; phi[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)]; phi[1]=1; phi[n_] := Product[phi[fa[n][[i, 1]], fa[n][[i, 2]]], {i, Length[fa[n]]}]; Select[Range[1000], IntegerQ[FU[#]/phi[#]] && PrimeQ[#] == False &]

%Y Cf. A060968, A201629, A235863, A182140.

%K nonn

%O 1,1

%A _José María Grau Ribas_, Jan 16 2014

%E a(29)-a(35) from _Amiram Eldar_, Nov 24 2023