A333131 Super pseudoprimes to both bases 2 and 3 (A333130) with more than two prime factors (counted with multiplicity).

11500521553, 13079177569, 52474339009, 168003672409, 229352039821, 280792563977, 318289021201, 428178002569, 918660756421, 2015841188197, 2367478228501, 2544457029601, 2639665216117, 3023595814801, 3457449931321, 3712164285421, 4348114583017, 6046196043229

Offset

1,1

Comments

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1085 (terms below 2^64)

Example

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).

Mathematica

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

Crossrefs

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

Sequence in context: A183709 A247312 A204780 * A172587 A172581 A213534

Adjacent sequences: A333128 A333129 A333130 * A333132 A333133 A333134

Keyword

nonn

Author

Amiram Eldar, Mar 08 2020

Status

approved