login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A218852 Numbers n for which sigma(n) = sigma(x) + sigma(y) + sigma(z), where n = x + y + z, with x, y, z all positive. 4
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 20 13:38 EDT 2021. Contains 348108 sequences. (Running on oeis4.)