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A241194
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Numerator of phi(p-1)/(p-1), where phi is Euler's totient function and p = prime(n).
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7
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1, 1, 1, 1, 2, 1, 1, 1, 5, 3, 4, 1, 2, 2, 11, 6, 14, 4, 10, 12, 1, 4, 20, 5, 1, 2, 16, 26, 1, 3, 2, 24, 8, 22, 18, 4, 4, 1, 41, 21, 44, 4, 36, 1, 3, 10, 8, 12, 56, 6, 14, 48, 4, 2, 1, 65, 33, 4, 22, 12, 46, 36, 16, 12, 4, 39, 8, 2, 86, 28, 5, 89, 20, 10, 2, 95
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OFFSET
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1,5
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COMMENTS
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The denominators are in A241195. The new minima of phi(p-1)/(p-1) occur at primes listed in A241196. The numerator and denominator of those terms are in A241197 and A241198.
For primes p>2, the fraction phi(p - 1)/(p - 1) has the maximum value = 1/2 if and only if p is in A019434. - Geoffrey Critzer, Dec 30 2014
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 117.
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LINKS
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FORMULA
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Asymptotic mean: lim_{m->oo} (1/m) * Sum_{n=1..m} a(n)/A241195(n) = 0.373955... (Artin's constant, A005596).
Asymptotic mean of inverse ratio: lim_{m->oo} (1/m) * Sum_{n=1..m} A241195(n)/a(n) = 2.826419... (Murata's constant, A065485). (End)
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MAPLE
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seq(numer(numtheory:-phi(ithprime(i)-1)/(ithprime(i)-1)), i=1..100); # Robert Israel, Jan 11 2015
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MATHEMATICA
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Numerator[Table[EulerPhi[p - 1]/(p - 1), {p, Prime[Range[100]]}]]
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PROG
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(PARI) lista(nn) = forprime(p=2, nn, print1(numerator(eulerphi(p-1)/(p-1)), ", ")); \\ Michel Marcus, Jan 03 2015
(Magma) [Numerator(EulerPhi(NthPrime(n)-1)/(NthPrime(n)-1)): n in [1..80]]; // Vincenzo Librandi, Apr 06 2015
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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