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

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, 29, 29, 29, 29, 30, 33, 33, 33, 34, 41, 41, 41, 41, 41, 41, 41, 46, 46, 46, 46, 46, 47, 51, 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

Offset: 1

Author

R. J. Mathar, Jun 30 2011

Keywords

• nonn

Comments

The discriminator D(3,n).

It appears that a(n) ~ n. Is there an explicit formula as for A016726? - M. F. Hasler, May 04 2016

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• P. Moree, H. Roskam, On an arithmetical function related to Euler's totient and the discriminator, Fib. Quart. 33 (4) (1995) 332-340

Crossrefs

Cf. A016726, A192420.

Programs

Maple

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} ;
end do: if nops(s) = n then return k; end if; end do: end proc:
A192419 := proc(n) dis(3,n) ; end proc:

Mathematica

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 *)

PARI

A192419(nMax)={my(S=[],a=1);vector(nMax, n, S=concat(S,n^3); while(#Set(S%a)M. F. Hasler, May 04 2016