A049605 Smallest k>1 such that k divides sigma(k*n).

6, 3, 2, 6, 2, 2, 2, 3, 6, 2, 2, 2, 2, 2, 2, 6, 2, 3, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 6, 2, 2, 2, 2, 2

Offset: 1

Author

Benoit Cloitre, Jul 26 2002

Keywords

• easy
• nonn

Comments

a(n) = 2, 3 or 6. For any m, a(A028983(m)) = 2. If a(m)=6 then m is a square but if m is a square a(m) is not necessarily 6, first example is 7: a(7^2)=3 (cf. A072864).

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A028983 (locations of 2), A067051 (locations of 3), A072862 (locations of 6).

Programs

Maple

A049605 := proc(n)
    for k from 2 do
        if modp(numtheory[sigma](k*n),k) = 0 then
            return k;
        end if;
    end do:
end proc: # R. J. Mathar, Oct 26 2015

Mathematica

sk[n_]:=Module[{k=2},While[!Divisible[DivisorSigma[1,k*n],k],k++];k]; sk /@ Range[110] (* Harvey P. Dale, Jan 04 2015 *)

PARI

a(n) = {k = 2; while(sigma(k*n) % k, k++); k ;} \\ Michel Marcus, Nov 21 2013