cp's OEIS Frontend

A127073 Composite numbers k that divide 3^k - 2^k - 1, excluding powers of 2, 3 and 7.

%I A127073 #12 Feb 16 2025 08:33:04
%S A127073 45,245,405,561,637,639,833,891,1105,1377,1576,1729,2465,2701,2821,
%T A127073 3321,3645,4753,5589,6345,6517,6601,7885,8911,10365,10585,12005,13833,
%U A127073 15841,17152,17265,18179,18721,21141,23552,25681,26411,29341,31213,31621
%N A127073 Composite numbers k that divide 3^k - 2^k - 1, excluding powers of 2, 3 and 7.
%C A127073 This sequence includes all the Carmichael numbers (A002997).
%C A127073 Prime p divides 3^p - 2^p - 1. Quotients (3^p - 2^p - 1)/p, where p = prime(n), are listed in A127071.
%C A127073 Numbers k such that k divides 3^k - 2^k - 1 are listed in A127072.
%C A127073 Pseudoprimes in A127072 include all the powers of the primes {2, 3, 7}.
%C A127073 Numbers k such that k^2 divides 3^k - 2^k - 1 are listed in A127074.
%C A127073 Numbers k such that k^3 divides 3^k - 2^k - 1 are 1, 4, 7, ...
%H A127073 Amiram Eldar, <a href="/A127073/b127073.txt">Table of n, a(n) for n = 1..10000</a>
%H A127073 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CarmichaelNumber.html">Carmichael number</a>.
%H A127073 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Pseudoprime.html">Pseudoprime</a>.
%t A127073 Select[Select[Range[2^15],!PrimeQ[ # ]&&IntegerQ[(3^#-2^#-1)/# ]&],!IntegerQ[Log[2,# ]]&&!IntegerQ[Log[3,# ]]&&!IntegerQ[Log[7,# ]]&]
%Y A127073 Cf. A002997, A127071, A127072, A127074.
%K A127073 nonn
%O A127073 1,1
%A A127073 _Alexander Adamchuk_, Jan 04 2007