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A002174
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Values taken by reduced totient function psi(n).
(Formerly M0986 N0370)
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16
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1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 28, 30, 32, 36, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60, 64, 66, 70, 72, 78, 80, 82, 84, 88, 90, 92, 96, 100, 102, 104, 106, 108, 110, 112, 116, 120, 126, 128, 130, 132, 136, 138, 140, 144, 148, 150, 156, 160, 162, 164, 166, 168
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OFFSET
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1,2
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COMMENTS
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If p is a Sophie Germain prime (A005384), then 2p is here. - T. D. Noe, Aug 13 2008
a(2445343) = 10^7, suggesting that Luca & Pomerance's lower bound may be closer to the truth than the upper bound. The fit exponent log a(n)/log n - 1 = 0.0957... in this case. - Charles R Greathouse IV, Jul 02 2017
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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n (log n)^0.086 << a(n) << n (log n)^0.36 where << is the Vinogradov symbol, see Luca & Pomerance. - Charles R Greathouse IV, Dec 28 2013
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MATHEMATICA
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(* warning: there seems to be no guarantee that no terms near the end are omitted! - Joerg Arndt, Dec 23 2014 *)
TakeWhile[Union@ Table[CarmichaelLambda@ n, {n, 10^6}], # <= 168 &] (* Michael De Vlieger, Mar 19 2016 *)
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PROG
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(PARI) list(lim)=my(v=List([1]), u, t); forprime(p=3, lim\3+1, u=List(); listput(u, p-1); while((t=u[#u]*p)<=lim, listput(u, t)); for(j=1, #v, for(i=1, #u, t=lcm(u[i], v[j]); if(t<=lim && t!=v[j], listput(v, t)))); v=List(Set(v))); forprime(p=lim\3+2, lim+1, listput(v, p-1)); v=List(Set(v)); for(i=1, #v, t=2*v[i]; if(t>lim, break); listput(v, t); while((t*=2)<=lim, listput(v, t))); Set(v) \\ Charles R Greathouse IV, Jun 23 2017
(PARI) is(n)=if(n%2, return(n==1)); my(f=factor(n), pe); for(i=1, #f~, if(n%(f[i, 1]-1)==0, next); pe=f[i, 1]^f[i, 2]; forstep(q=2*pe+1, n+1, 2*pe, if(n%(q-1)==0 && isprime(q), next(2))); return(0)); 1 \\ Charles R Greathouse IV, Jun 25 2017
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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