A218852 - OEIS

%I #21 Jun 22 2020 17:00:43

%S 5,7,10,13,14,15,16,19,20,21,25,26,27,28,31,32,33,34,35,38,39,40,42,

%T 43,44,45,46,49,50,51,52,54,55,56,57,58,61,62,63,64,65,66,68,69,70,73,

%U 74,75,76,77,78,80,81,82,84,85,86,87,88,90,91,92,93,94,95,96

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

%C Contains the greater of every twin prime pair.

%H Harvey P. Dale, <a href="/A218852/b218852.txt">Table of n, a(n) for n = 1..400</a>

%e sigma(1) + sigma(1) + sigma(3) = sigma(5) = 6.

%e sigma(2) + sigma(2) + sigma(6) = sigma(10) = 18.

%e *sigma(2) + sigma(8) + sigma(30) = sigma(40) = 90.

%e *sigma(6) + sigma(10) + sigma(24) = sigma(40) = 90.

%e sigma(8) + sigma(8) + sigma(24) = sigma(40) = 90.

%e Hence, 5, 10 and 40 are in the sequence.

%e Note that (*) means that (x+y+z) divides xyz as well.

%p isA218852 := proc(n)

%p     local x,y,z ;

%p     for x from 1 to n-2 do

%p         for y from x to n-x-1 do

%p             z := n-x-y ;

%p             if numtheory[sigma](x)+numtheory[sigma](y)+numtheory[sigma](z) = numtheory[sigma](n) then

%p                 return true;

%p             end if;

%p         end do:

%p     end do:

%p     return false;

%p end proc:

%p for n from 3 to 120 do

%p     if isA218852(n) then

%p         printf("%d,",n);

%p     end if;

%p end do: # _R. J. Mathar_, Nov 07 2012

%t 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 *)

%Y Cf. A000203, A211223, A218980.

%K nonn

%O 1,1

%A _Jon Perry_, Nov 07 2012