

A333130


Numbers that are super pseudoprimes to both bases 2 and 3.


2



2701, 18721, 31621, 49141, 83333, 90751, 104653, 226801, 282133, 653333, 665281, 721801, 873181, 1373653, 1530787, 1537381, 1584133, 1690501, 1755001, 1987021, 2008597, 2035153, 2284453, 2746589, 2944261, 3059101, 3116107, 3363121, 3375041, 3375487, 4082653, 4314967
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OFFSET

1,1


COMMENTS

The first term that has more than 2 prime factors is a(1067) = A333131(1) = 11500521553.
The first term that is also a Carmichael number is a(1131) = 13079177569.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


EXAMPLE

2701 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 all primes: 37 and 73.


MATHEMATICA

pspQ[n_] := CompositeQ[n] && AllTrue[Rest @ Divisors[n], PowerMod[2, #  1, #] == 1 && PowerMod[3, #  1, #] == 1 &]; Select[Range[10^6], pspQ]


CROSSREFS

Intersection of A050217 and A328662.
Subsequence of A001567, A005935, A052155 and A153513.
Sequence in context: A230752 A246888 A153513 * A214016 A254513 A254506
Adjacent sequences: A333127 A333128 A333129 * A333131 A333132 A333133


KEYWORD

nonn


AUTHOR

Amiram Eldar, Mar 08 2020


STATUS

approved



