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A127073
Composite numbers k that divide 3^k - 2^k - 1, excluding powers of 2, 3 and 7.
9
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
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
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Jan 04 2007
STATUS
approved