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

Author

Jon Perry, Nov 07 2012

Keywords

• nonn

Comments

Contains the greater of every twin prime pair.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000203, A211223, A218980.

Programs

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 *)