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A122783 Nonprimes k > 0 such that 6^k==6 (mod k).

%I A122783 #9 Jan 06 2022 16:19:23
%S A122783 1,6,10,15,21,30,35,105,185,190,217,231,301,430,435,481,561,777,1105,
%T A122783 1111,1221,1261,1333,1729,1866,2121,2465,2553,2701,2821,2955,3421,
%U A122783 3565,3589,3885,3913,4123,4495,5061,5565,5662,5713,6531,6533,6601
%N A122783 Nonprimes k > 0 such that 6^k==6 (mod k).
%C A122783 Theorem: If both numbers q and 2q-1 are primes then n=q*(2q-1) is in the sequence iff q<5 or q is of the form 12k+1. 6,15,2701,18721,49141,104653,226801,665281,... are such terms.
%H A122783 Harvey P. Dale, <a href="/A122783/b122783.txt">Table of n, a(n) for n = 1..1000</a>
%e A122783 1 is a term since 6^1 = 6 is congruent to 6 mod 1.
%e A122783 2 is not a term since although 6^2 === 6 (mod 2), 2 IS a prime.
%e A122783 4 is not a term since 6^4 = 1296 == 0 mod 4, while 6 == 2 (mod 4).
%e A122783 6 is a term since 6^6 = 46656 == 0 (mod 6), and 6 == 0 (mod 6).
%e A122783 10 is a term because 6^10 = 60466176 == 6 (mod 10)
%t A122783 Select[Range[7000], ! PrimeQ[ # ] && Mod[6^#, # ] == Mod[6, # ] &]
%t A122783 Join[{1,6},Select[Range[7000],!PrimeQ[#]&&PowerMod[6,#,#]==6&]] (* _Harvey P. Dale_, Jan 06 2022 *)
%Y A122783 Cf. A005937.
%K A122783 easy,nonn
%O A122783 1,2
%A A122783 _Farideh Firoozbakht_, Sep 12 2006
%E A122783 Examples added by _N. J. A. Sloane_, Jan 06 2022