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A307711 a(n) is the least number k such that exactly fraction 1/n of the members of the reduced residue system mod k are prime, or 0 if there is no such k. 2
3, 31, 97, 331, 1009, 3067, 11513, 27403, 64621, 185617, 480853, 1333951, 3524431, 9558361, 26080333, 70411483, 189961939 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(n) is the least number k, if any exists, such that A000010(k)/A048865(k) = n.

a(n) = A307712(m) for the least m such that A307713(m)=n.

LINKS

Table of n, a(n) for n=2..18.

FORMULA

n*A048865(a(n)) = A000010(a(n)).

EXAMPLE

Of the 30 members of the reduced residue system mod 31, exactly one-third, namely 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, are prime.  31 is the least number with this property, so a(3) = 31.

MAPLE

f:= proc(n) uses numtheory;

  phi(n)/(pi(n) - nops(factorset(n)));

end proc:

N:= 13: # to get a(2)..a(N)

R:= Array(2..N): count:= 0:

for k from 3 while count < N-1 do

  v:= f(k);

  if v::integer and v <= N and R[v] = 0 then

     R[v]:= k;

     count:= count+1;

  fi

od:

convert(R, list);

MATHEMATICA

With[{s = Table[EulerPhi[n]/Count[Prime@ Range@ PrimePi@ n, _?(GCD[#, n] == 1 &)], {n, 3, 10^4}]}, Array[2 + FirstPosition[s, #][[1]] &, Max@ Select[s, IntegerQ] - 1, 2]] (* Michael De Vlieger, Apr 23 2019 *)

CROSSREFS

Cf. A000010, A048865, A307712.

Sequence in context: A152417 A182232 A294973 * A077547 A104312 A326736

Adjacent sequences:  A307708 A307709 A307710 * A307712 A307713 A307714

KEYWORD

nonn,more

AUTHOR

J. M. Bergot and Robert Israel, Apr 23 2019

STATUS

approved

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Last modified August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)