A333131 - OEIS

%I #12 Mar 09 2020 03:15:10

%S 11500521553,13079177569,52474339009,168003672409,229352039821,

%T 280792563977,318289021201,428178002569,918660756421,2015841188197,

%U 2367478228501,2544457029601,2639665216117,3023595814801,3457449931321,3712164285421,4348114583017,6046196043229

%N Super pseudoprimes to both bases 2 and 3 (A333130) with more than two prime factors (counted with multiplicity).

%C Up to 2^64 all the 1085 terms are nonsquarefree, 2 terms have 4 prime factors: a(163) = 18362297383286473 = 3037 * 6073 * 9109 * 109297 and a(651) = 2587580959818925201 = 18121 * 36241 * 54361 * 72481, and no term have more than 4 prime factors.

%H Amiram Eldar, <a href="/A333131/b333131.txt">Table of n, a(n) for n = 1..1085</a> (terms below 2^64)

%e 11500521553 is a term since it is a Fermat pseudoprime to both bases 2 and 3, and its proper divisors that are larger than 1 are either primes (937, 1873, 6553) or Fermat pseudoprimes to both bases 2 and 3 (1755001, 6140161, 12273769, 11500521553).

%t pspQ[n_] := PrimeOmega[n] > 2 && AllTrue[Rest @ Divisors[n], PowerMod[2, # - 1, #] == 1 && PowerMod[3, # - 1, #] == 1 &]; seq = {}; Do[If[pspQ[n], AppendTo[seq, n]], {n, 1, 6*10^10}]; seq

%Y Subsequence of A001567, A005935, A050217, A052155, A153513, A178997, A328662, A328663, A333130.

%K nonn

%O 1,1

%A _Amiram Eldar_, Mar 08 2020