A107924 Even numbers n such that n^2 is an arithmetic number.

296, 536, 632, 872, 1208, 1304, 1544, 2072, 2216, 2648, 2984, 3584, 3656, 3752, 3848, 3896, 3904, 3992, 4328, 4424, 4568, 4904, 5624, 5672, 5912, 6008, 6104, 6584, 6968, 7016, 7256, 7352, 7928, 8216, 8264, 8456, 8696, 8896, 8936, 9032, 9128, 9176, 9368

Offset: 1

Author

Zak Seidov, Jun 10 2005

Keywords

• nonn
• easy

Comments

Odd numbers with this property are much more numerous, cf. A107925, A003601 (arithmetic number).

Links

• R. J. Mathar, Michael De Vlieger, Table of n, a(n) for n = 1..10778 (first 443 terms from R. J. Mathar)

Crossrefs

Cf. A003601, A107925.

Programs

Maple

isA107924 := proc(n)
    if type(n,'even') then
        dvs := numtheory[divisors](n^2) ;
        add(d,d=dvs)/nops(dvs) ;
        if type(%,'integer') then
            true;
        else
            false;
        end if;
    else
        false;
    end if;
end proc:
n := 1 :
for k from 2 to 100000 do
    if isA107924(k) then
        printf("%d %d\n",n,k) ;
        n := n+1 ;
    end if;
end do: # create b-file, R. J. Mathar, Jul 28 2014

Mathematica

Select[Range[2, 10000, 2], Mod[DivisorSigma[1, #^2], DivisorSigma[0, #^2]]==0&]