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
KEYWORD
nonn
AUTHOR
Jon Perry, Nov 07 2012
STATUS
approved