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