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

1,1

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.

Mathematica

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

Crossrefs

Cf. A002997, A127071, A127072, A127074.

Sequence in context: A169717 A246420 A172118 * A089549 A178540 A351534

Adjacent sequences: A127070 A127071 A127072 * A127074 A127075 A127076

Keyword

nonn

Author

Alexander Adamchuk, Jan 04 2007

Status

approved