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A346316
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Composite numbers with primitive root 6.
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2
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121, 169, 289, 1331, 1681, 2197, 3481, 3721, 4913, 6241, 6889, 7921, 10609, 11449, 11881, 12769, 14641, 16129, 17161, 18769, 22801, 24649, 28561, 32041, 39601, 49729, 51529, 52441, 54289, 63001, 66049, 68921, 73441, 76729, 83521, 120409, 134689, 139129, 157609
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OFFSET
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1,1
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COMMENTS
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An alternative description: Numbers k such that 1/k in base 6 generates a repeating fraction with period phi(n) and n/2 < phi(n) < n-1.
For example, in base 6, 1/121 has repeat length 110 = phi(121) which is > 121/2 but less than 121-1.
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LINKS
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FORMULA
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MAPLE
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isA033948 := proc(n)
if n in {1, 2, 4} then
true;
elif type(n, 'odd') and nops(numtheory[factorset](n)) = 1 then
true;
elif type(n, 'even') and type(n/2, 'odd') and nops(numtheory[factorset](n/2)) = 1 then
true;
else
false;
end if;
end proc:
isA167794 := proc(n)
if not isA033948(n) or n = 1 then
false;
elif numtheory[order](6, n) = numtheory[phi](n) then
true;
else
false;
end if;
end proc:
option remember;
local a;
if n = 1 then
121;
else
for a from procname(n-1)+1 do
if not isprime(a) and isA167794(a) then
return a;
end if;
end do:
end if;
end proc:
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MATHEMATICA
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Select[Range[160000], CompositeQ[#] && PrimitiveRoot[#, 6] == 6 &] (* Amiram Eldar, Jul 13 2021 *)
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PROG
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(PARI) isok(m) = (m>1) && !isprime(m) && (gcd(m, 6)==1) && (znorder(Mod(6, m))==eulerphi(m)); \\ Michel Marcus, Aug 12 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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