A333130 - OEIS

%I #9 Mar 09 2020 03:15:14

%S 2701,18721,31621,49141,83333,90751,104653,226801,282133,653333,

%T 665281,721801,873181,1373653,1530787,1537381,1584133,1690501,1755001,

%U 1987021,2008597,2035153,2284453,2746589,2944261,3059101,3116107,3363121,3375041,3375487,4082653,4314967

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

%C The first term that has more than 2 prime factors is a(1067) = A333131(1) = 11500521553.

%C The first term that is also a Carmichael number is a(1131) = 13079177569.

%H Amiram Eldar, <a href="/A333130/b333130.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

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

%Y Intersection of A050217 and A328662.

%Y Subsequence of A001567, A005935, A052155 and A153513.

%K nonn

%O 1,1

%A _Amiram Eldar_, Mar 08 2020