A218852 Numbers n for which sigma(n) = sigma(x) + sigma(y) + sigma(z), where n = x + y + z, with x, y, z all positive.

5, 7, 10, 13, 14, 15, 16, 19, 20, 21, 25, 26, 27, 28, 31, 32, 33, 34, 35, 38, 39, 40, 42, 43, 44, 45, 46, 49, 50, 51, 52, 54, 55, 56, 57, 58, 61, 62, 63, 64, 65, 66, 68, 69, 70, 73, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96

Offset

1,1

Comments

Contains the greater of every twin prime pair.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..400

Example

sigma(1) + sigma(1) + sigma(3) = sigma(5) = 6.
sigma(2) + sigma(2) + sigma(6) = sigma(10) = 18.
*sigma(2) + sigma(8) + sigma(30) = sigma(40) = 90.
*sigma(6) + sigma(10) + sigma(24) = sigma(40) = 90.
sigma(8) + sigma(8) + sigma(24) = sigma(40) = 90.
Hence, 5, 10 and 40 are in the sequence.
Note that (*) means that (x+y+z) divides xyz as well.

Maple

isA218852 := proc(n)
    local x, y, z ;
    for x from 1 to n-2 do
        for y from x to n-x-1 do
            z := n-x-y ;
            if numtheory[sigma](x)+numtheory[sigma](y)+numtheory[sigma](z) = numtheory[sigma](n) then
                return true;
            end if;
        end do:
    end do:
    return false;
end proc:
for n from 3 to 120 do
    if isA218852(n) then
        printf("%d, ", n);
    end if;
end do: # R. J. Mathar, Nov 07 2012

Mathematica

xyzQ[n_]:=Module[{ips=Total/@(DivisorSigma[1, #]&/@IntegerPartitions[n, {3}])}, Total[Boole[DivisorSigma[1, n]==#&/@ips]]>0]; Select[Range[ 100], xyzQ] (* Harvey P. Dale, Jun 22 2020 *)

Crossrefs

Cf. A000203, A211223, A218980.

Sequence in context: A293867 A129189 A066513 * A028810 A097700 A172321

Adjacent sequences: A218849 A218850 A218851 * A218853 A218854 A218855

Keyword

nonn

Author

Jon Perry, Nov 07 2012

Status

approved