A127071 - OEIS

%I #10 Sep 08 2022 08:45:29

%S 2,6,42,294,15918,122010,7588770,61144062,4092816966,2366546223930,

%T 19924878993558,12169831579784970,889585223857256850,

%U 7633882758103350126,565719451451489679414,365721616201373974378410

%N Quotients (3^p - 2^p - 1)/p, where p = prime(n).

%C Prime p divides 3^p - 2^p - 1. 42 = 2*3*7 divides a(n) for n>2.

%C Numbers n such that n divides 3^n - 2^n - 1 are listed in A127072.

%C Pseudoprimes in A127072 include all powers of primes {2,3,7} and some composite numbers that are listed in A127073.

%C Numbers n such that n^2 divides 3^n - 2^n - 1 are listed in A127074.

%C Numbers n such that n^3 divides 3^n - 2^n - 1 are {1,4,7,...}.

%H G. C. Greubel, <a href="/A127071/b127071.txt">Table of n, a(n) for n = 1..315</a>

%F a(n) = (3^prime(n) - 2^prime(n) - 1)/prime(n).

%p seq((3^ithprime(n) -2^ithprime(n) -1)/(ithprime(n)), n=1..20); # _G. C. Greubel_, Aug 11 2019

%t Table[(3^Prime[n]-2^Prime[n]-1)/Prime[n],{n,1,20}]

%o (PARI) vector(20, n, p=prime; (3^p(n) - 2^p(n) -1)/p(n) ) \\ _G. C. Greubel_, Aug 11 2019

%o (Magma) p:=NthPrime; [(3^p(n) -2^p(n) -1)/p(n): n in [1..20]]; // _G. C. Greubel_, Aug 11 2019

%o (Sage) p=nth_prime; [(3^p(n) -2^p(n) -1)/p(n) for n in (1..20)] # _G. C. Greubel_, Aug 11 2019

%Y Cf. A127072, A127073, A127074.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Jan 04 2007