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Carmichael numbers that are not == 1 mod 12. There are 69 Carmichael numbers out to 2*m+1, m=2*10^6 and all but the above 9 are 1 mod 12.
1

%I #6 Nov 12 2015 21:03:10

%S 561,2465,8911,62745,162401,656601,1024651,1152271,1909001,5444489,

%T 5481451,10267951,11921001,14913991,19384289,26719701,45318561,

%U 64377991,67902031,84350561,139952671,151530401,174352641,178482151,221884001,230996949,275283401,368113411,395044651

%N Carmichael numbers that are not == 1 mod 12. There are 69 Carmichael numbers out to 2*m+1, m=2*10^6 and all but the above 9 are 1 mod 12.

%H Charles R Greathouse IV, <a href="/A110889/b110889.txt">Table of n, a(n) for n = 1..25567</a>

%e 8911=7*19*67=5 mod 12.

%p with(numtheory); CM:=[]: for z from 1 to 1 do for m from 1 to 2000000 do n:=2*m+1; if not(isprime(n)) and issqrfree(n) then PF:=factorset(n); cmb:=true; for x in PF do if (n-1) mod (x-1) > 0 then cmb:=false fi od; if cmb then CM:=[op(CM),n]; fi; fi; #not od; #m od; #z select(proc(z) not(z mod 12 = 1) end, CM);

%Y Cf. A002997.

%K nonn

%O 1,1

%A _Walter Kehowski_, Sep 20 2005

%E a(12)-a(29) from _Charles R Greathouse IV_, Nov 12 2015