A307712 Numbers k such that the fraction of primes in the reduced residue system mod k is the reciprocal of an integer.

3, 4, 5, 6, 7, 9, 10, 15, 21, 31, 45, 49, 58, 65, 82, 86, 92, 97, 101, 105, 116, 183, 187, 196, 201, 207, 217, 238, 297, 305, 308, 310, 320, 331, 380, 425, 583, 649, 675, 855, 964, 972, 974, 978, 993, 996, 998, 1009, 1016, 1017, 1041, 1068, 1093, 1112, 1117, 1123, 1129, 1161, 1184, 1368, 1403

Offset

1,1

Comments

Numbers k such that A000010(k)/A048865(k) is an integer.

The corresponding integers are in A307713.

Links

Robert Israel, Table of n, a(n) for n = 1..600

Example

a(6)=9 is in the sequence because 3 of the 6 reduced residues mod 9 are prime, and 3 divides 6. The reduced residues are 1,2,4,5,7,8, of which 2,5,7 are prime.
8 is not in the sequence because 3 of the 4 reduced residues mod 8 are prime, and 3 does not divide 4.

Maple

filter:= proc(n) uses numtheory;
type(phi(n)/(pi(n) - nops(factorset(n))), integer);
end proc:
select(filter, [$3..10000]);

Mathematica

Select[Range[3, 1500], Function[n, IntegerQ[EulerPhi[n]/Count[Prime@ Range@ PrimePi@ n, _?(GCD[#, n] == 1 &)]]]] (* Michael De Vlieger, Apr 23 2019 *)

Crossrefs

Cf. A000010, A048865, A307711, A307713.

Sequence in context: A026438 A026442 A334763 * A048869 A039051 A047564

Adjacent sequences: A307709 A307710 A307711 * A307713 A307714 A307715

Keyword

nonn

Author

Robert Israel, Apr 23 2019

Status

approved