A333130 Numbers that are super pseudoprimes to both bases 2 and 3.

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

Offset: 1

Author

Amiram Eldar, Mar 08 2020

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Intersection of A050217 and A328662.

Subsequence of A001567, A005935, A052155 and A153513.

Programs

Mathematica

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