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A333131 Super pseudoprimes to both bases 2 and 3 (A333130) with more than two prime factors (counted with multiplicity). 2
11500521553, 13079177569, 52474339009, 168003672409, 229352039821, 280792563977, 318289021201, 428178002569, 918660756421, 2015841188197, 2367478228501, 2544457029601, 2639665216117, 3023595814801, 3457449931321, 3712164285421, 4348114583017, 6046196043229 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 23 08:40 EDT 2021. Contains 348211 sequences. (Running on oeis4.)