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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A068580 A110994 A015833 * A003429 A076860 A283592
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 06 2002
STATUS
approved

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Last modified April 19 14:10 EDT 2024. Contains 371792 sequences. (Running on oeis4.)