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

45, 245, 405, 561, 637, 639, 833, 891, 1105, 1377, 1576, 1729, 2465, 2701, 2821, 3321, 3645, 4753, 5589, 6345, 6517, 6601, 7885, 8911, 10365, 10585, 12005, 13833, 15841, 17152, 17265, 18179, 18721, 21141, 23552, 25681, 26411, 29341, 31213, 31621

Offset: 1

Author

Alexander Adamchuk, Jan 04 2007

Keywords

• nonn

Comments

This sequence includes all the Carmichael numbers (A002997).

Prime p divides 3^p - 2^p - 1. Quotients (3^p - 2^p - 1)/p, where p = prime(n), are listed in A127071.

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

Pseudoprimes in A127072 include all the powers of the primes {2, 3, 7}.

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

Numbers k such that k^3 divides 3^k - 2^k - 1 are 1, 4, 7, ...

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Carmichael number.
• Eric Weisstein's World of Mathematics, Pseudoprime.

Crossrefs

Cf. A002997, A127071, A127072, A127074.

Programs

Mathematica

Select[Select[Range[2^15],!PrimeQ[ # ]&&IntegerQ[(3^#-2^#-1)/# ]&],!IntegerQ[Log[2,# ]]&&!IntegerQ[Log[3,# ]]&&!IntegerQ[Log[7,# ]]&]