A072022 Smallest x such that the number of nonprimes (i.e., 1 and composites) in the reduced residue set (RSS(x)) of x equals n, or 0 if there are no such x.

1, 5, 7, 15, 26, 11, 13, 38, 102, 17, 19, 25, 0, 23, 35, 144, 74, 198, 29, 31, 75, 57, 104, 94, 37, 55, 69, 41, 43, 118, 0, 47, 81, 128, 87, 134, 53, 93, 480, 146, 77, 59, 61, 117, 111, 166, 172, 67, 250, 91, 71, 73, 350, 194, 129, 202, 79, 206, 212, 83, 214, 153, 218

Offset

1,2

Comments

See A074915 for a bound on A048864(x) which allows the establishment of a search range for a(n). - Giovanni Resta, Feb 25 2020

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Abhijit A J, A. Satyanarayana Reddy, Number of non-primes in the set of units modulo n, arXiv:1907.09908 [math.GM], 2019.

Formula

a(n) = min{x; A048864(x)=n}; a(n)=0 if no such number exists.

Example

n = 15: RRS(15) = {1,2,4,7,8,11,13,14} of which nonprimes = cRRS(15) = {1,4,8,14}, i.e., 4 terms; 15 is the smallest such number, so a(4) = 15. a(m) = 0 for m = {13, 31, 70, 119, 189, 210, 235, 236}.

Mathematica

f[x_] := EulerPhi[x]-PrimePi[x]+Length[FactorInteger[x]] t=Table[0, {256}]; Do[s=f[n]; If[s<257&&t[[s]]==0, t[[s]]=n], {n, 3, 1000000}]; t
(* Second program: *)
With[{s = Table[Count[Range[n - 1], k_ /; And[CoprimeQ[k, n], ! PrimeQ@ k]], {n, 10^3}]}, Function[{t, u}, Take[#, 63] &@ Join[{1}, Rest@ ReplacePart[t, Map[# -> Lookup[u, #][[1]] &, Rest@ Keys@ u]]]] @@ {ConstantArray[0, Max@ s], KeySort@ PositionIndex@ s}] (* Michael De Vlieger, Jul 30 2017 *)

Prog

(PARI) f(n) = eulerphi(n) - (primepi(n) - omega(n)); \\ A048864
a(n) = {my(k=1); while (f(k) != n, k++); k; } \\ Michel Marcus, Aug 07 2019

Crossrefs

Cf. A048864, A072023, A074915.

Sequence in context: A068580 A110994 A015833 * A003429 A076860 A283592

Adjacent sequences: A072019 A072020 A072021 * A072023 A072024 A072025

Keyword

nonn

Author

Labos Elemer, Jun 06 2002

Status

approved