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A192419 Smallest k such that 1^3, 2^3, 3^3,... n^3 are distinct modulo k.

%I A192419 #22 Jan 05 2025 19:51:39
%S A192419 1,2,3,5,5,6,10,10,10,10,11,15,15,15,15,17,17,22,22,22,22,22,23,29,29,
%T A192419 29,29,29,29,30,33,33,33,34,41,41,41,41,41,41,41,46,46,46,46,46,47,51,
%U A192419 51,51,51,53,53,55,55,58,58,58,59,66,66,66,66,66,66,66,69,69,69,71,71,82,82,82,82,82,82,82,82,82,82
%N A192419 Smallest k such that 1^3, 2^3, 3^3,... n^3 are distinct modulo k.
%C A192419 The discriminator D(3,n).
%C A192419 It appears that a(n) ~ n. Is there an explicit formula as for A016726? - _M. F. Hasler_, May 04 2016
%H A192419 Harvey P. Dale, <a href="/A192419/b192419.txt">Table of n, a(n) for n = 1..1000</a>
%H A192419 P. Moree, H. Roskam, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/33-4/moree.pdf">On an arithmetical function related to Euler's totient and the discriminator</a>, Fib. Quart. 33 (4) (1995) 332-340
%p A192419 dis := proc(j,n) local k,s,i; for k from 1 do s := {} ; for i from 1 to n do s := s union { (i^j) mod k} ;
%p A192419 end do: if nops(s) = n then return k; end if; end do: end proc:
%p A192419 A192419 := proc(n) dis(3,n) ; end proc:
%t A192419 dmk[n_]:=Module[{k=1,res},While[res=Table[PowerMod[i,3,k],{i,n}]; Length[ res]!= Length[Union[res]],k++];k]; Array[dmk,90] (* _Harvey P. Dale_, Jan 28 2013 *)
%o A192419 (PARI) A192419(nMax)={my(S=[],a=1);vector(nMax, n, S=concat(S,n^3); while(#Set(S%a)<n, a++); a)} \\ _M. F. Hasler_, May 04 2016
%Y A192419 Cf. A016726, A192420.
%K A192419 nonn
%O A192419 1,2
%A A192419 _R. J. Mathar_, Jun 30 2011