A072864 -id:A072864 - cp's OEIS frontend

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

Benoit Cloitre, Jul 26 2002

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).

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

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

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

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

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

A074216 Squares satisfying sigma(n)==0 (mod 3).

Original entry on oeis.org

49, 169, 196, 361, 441, 676, 784, 961, 1225, 1369, 1444, 1521, 1764, 1849, 2704, 3136, 3249, 3721, 3844, 3969, 4225, 4489, 4900, 5329, 5476, 5776, 5929, 6084, 6241, 7056, 7396, 8281, 8649, 9025, 9409, 10609, 10816, 11025, 11881, 12321, 12544

Offset: 1

Benoit Cloitre, Sep 17 2002

nonn

Seems to contain all numbers of form k^2*p^2 where p are primes in A002476, k is not congruent to p and >=1.

Squares in A067051. - Michel Marcus, Dec 26 2013

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A067051, A065764.

[n: n in [1..14161]|IsSquare(n) and DivisorSigma(1,n) mod 3 eq 0 ]; // Marius A. Burtea, Aug 17 2019

with(numtheory); A074216:=n->`if`(1-ceil(sigma(n^2)/3)+floor(sigma(n^2)/3)=1,n^2,NULL); seq(A074216(n), n=1..200); # Wesley Ivan Hurt, Dec 06 2013

Select[Range[150]^2,Divisible[DivisorSigma[1,#],3]&] (* Harvey P. Dale, Jul 10 2012 *)

isok(n) = issquare(n) && !(sigma(n) % 3); \\ Michel Marcus, Aug 17 2019

Conjecture: a(n) = A072864(n)^2. - R. J. Mathar, May 19 2020

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI