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A187731
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Numbers n such that rad(phi(n)) divides n-1.
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6
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1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 37, 41, 43, 47, 51, 53, 59, 61, 67, 71, 73, 79, 83, 85, 89, 91, 97, 101, 103, 107, 109, 113, 127, 131, 133, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 247, 251, 255, 257, 259
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OFFSET
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1,2
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COMMENTS
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Subsequence of A003277 (cyclic numbers).
Let L(x) = exp(log x log log log x/log log x). McNew shows that there are at most x/L(x)^(1+o(1)) members of this sequence up to x. - Charles R Greathouse IV, Oct 08 2012
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LINKS
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EXAMPLE
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15 is in the sequence because phi(15)=8, rad(8)=2 and 2 divides 15-1.
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MATHEMATICA
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rad[n_]:=Times@@Transpose[FactorInteger[n]][[1]]; Select[Range[1000], Mod[#-1, rad[EulerPhi[#]]]==0&]
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PROG
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(PARI) rad(n)=n=factor(n); prod(i=1, #n[, 1], n[i, 1]);
(PARI) is(n)=my(p=eulerphi(n), g=n); n--; while((g=gcd(p, g))>1, p/=g); p==1 && n \\ Charles R Greathouse IV, Mar 03 2014
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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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