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A307712
Numbers k such that the fraction of primes in the reduced residue system mod k is the reciprocal of an integer.
3
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
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
KEYWORD
nonn
AUTHOR
Robert Israel, Apr 23 2019
STATUS
approved