A127071 Quotients (3^p - 2^p - 1)/p, where p = prime(n).

2, 6, 42, 294, 15918, 122010, 7588770, 61144062, 4092816966, 2366546223930, 19924878993558, 12169831579784970, 889585223857256850, 7633882758103350126, 565719451451489679414, 365721616201373974378410

Offset: 1

Author

Alexander Adamchuk, Jan 04 2007

Keywords

• nonn

Comments

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

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

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

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

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..315

Crossrefs

Cf. A127072, A127073, A127074.

Programs

Magma

p:=NthPrime; [(3^p(n) -2^p(n) -1)/p(n): n in [1..20]]; // G. C. Greubel, Aug 11 2019

Maple

seq((3^ithprime(n) -2^ithprime(n) -1)/(ithprime(n)), n=1..20); # G. C. Greubel, Aug 11 2019

Mathematica

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

PARI

vector(20, n, p=prime; (3^p(n) - 2^p(n) -1)/p(n) ) \\ G. C. Greubel, Aug 11 2019

Sage

p=nth_prime; [(3^p(n) -2^p(n) -1)/p(n) for n in (1..20)] # G. C. Greubel, Aug 11 2019

Formula

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