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Second prime factor of x = 3^p - 2^p when p is prime and omega(x) >= 2.
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%I #20 Jun 30 2023 03:51:17

%S 71,331,29927,745181,2002867877,50642213021,32309,1196347,303168989,

%T 203778431,17685389279,111998979662707645844109121,645845309,146309,

%U 499,706132008101135602203621405289,59813046375181769306016700165290169537,1016611,28463,128621,2381120538437

%N Second prime factor of x = 3^p - 2^p when p is prime and omega(x) >= 2.

%C All prime factors of 3^p - 2^p, where p is prime, are = 1 (mod p).

%H Amiram Eldar, <a href="/A089163/b089163.txt">Table of n, a(n) for n = 1..93</a>

%H Chris Caldwell, <a href="https://t5k.org/mersenne/index.html">Mersenne Primes: History, Theorems and Lists</a>.

%e 3^11 - 2^11 = 23*331. The second prime factor is 331. These factors are congruent to 1 mod 11.

%o (PARI) apmapm1(a,b,n,d) = { c=0; forprime(x=2,n, c++; y = a^x-b^x; f=factor(y); v=component(f,1); ln = length(v); if(ln>=d,print(v[d]",")); ) }

%Y Cf. A001047.

%K nonn

%O 1,1

%A _Cino Hilliard_, Dec 06 2003

%E Name corrected by _Michel Marcus_, Dec 16 2022

%E a(18)-a(21) from _Amiram Eldar_, Jun 30 2023