A123623 Smallest k>1 such that mu(n*k) = mu(n), where mu=A008683.

6, 15, 10, 2, 6, 35, 6, 2, 2, 21, 6, 2, 6, 15, 14, 2, 6, 2, 6, 2, 10, 15, 6, 2, 2, 15, 2, 2, 6, 77, 6, 2, 10, 15, 6, 2, 6, 15, 10, 2, 6, 55, 6, 2, 2, 15, 6, 2, 2, 2, 10, 2, 6, 2, 6, 2, 10, 15, 6, 2, 6, 15, 2, 2, 6, 35, 6, 2, 10, 33, 6, 2, 6, 15, 2, 2, 6, 35, 6, 2, 2, 15, 6, 2, 6, 15, 10, 2, 6, 2, 6, 2

Offset

1,1

Comments

a(n) = A123624(n) / n.

From Robert Israel, Apr 02 2017: (Start)

If n is squarefree, a(n) is the product of the least two primes coprime to n.

Otherwise a(n) = 2. (End)

Links

R. Zumkeller, Table of n, a(n) for n = 1..10000

Maple

a:= proc(n) local r, p, count;
  if not numtheory:-issqrfree(n) then return 2 fi;
  r:= 1; count:= 0; p:= 1;
  do
    p:= nextprime(p);
    if n mod p > 0 then
      count:= count+1;
      r:= r*p;
      if count = 2 then return r fi
    fi
  od
end proc:
map(a, [$1..1000]); # Robert Israel, Apr 02 2017

Mathematica

a[n_] := Module[{r = 1, p = 1, count = 0}, If[!SquareFreeQ[n], Return[2]]; While[True, p = NextPrime[p]; If[Mod[n, p] > 0, count++; r = r*p; If[count == 2, Return[r]]]]]; Array[a, 100] (* Jean-François Alcover, Feb 13 2018, after Robert Israel *)

Crossrefs

Cf. A093316.

Sequence in context: A351369 A070870 A202749 * A240990 A215739 A161397

Adjacent sequences: A123620 A123621 A123622 * A123624 A123625 A123626

Keyword

nonn

Author

Reinhard Zumkeller, Oct 03 2006

Extensions

Name corrected by Robert Israel, Apr 02 2017

Status

approved