A211217 Maximum of sigma(x) * sigma(y), where x + y = n.

1, 3, 9, 12, 21, 28, 49, 48, 84, 72, 144, 96, 180, 156, 225, 195, 336, 234, 420, 364, 504, 360, 784, 432, 672, 672, 868, 576, 1092, 744, 1176, 936, 1209, 1008, 1680, 992, 1638, 1440, 1860, 1344, 2340, 1344, 2520, 1920, 2232, 1680, 3600, 1860, 3024, 2400

Offset: 2

Author

Paolo P. Lava, Apr 05 2012

Keywords

• nonn

Examples

			For n=83 the maximum product is reached when 35 and 48 (35+48=83) are considered: sigma(35)*sigma(48) = 48*124 = 5952.
For n=99 the maximum product is reached when 36 and 63 (36+63=99) are considered: sigma(36)*sigma(63) = 91*104 = 9464.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 2..10000
• Paolo P. Lava, Plot of the first 10000 terms of the sequence

Crossrefs

Cf. A211216, A211218, A211219.

Programs

Maple

with(combstruct); with(numtheory);
A211217:=proc(i)
local a,b,j,n,t;
for n from 2 to i do
  t:=0;
  for j from 0 to floor(n/2) do
    a:=n-j; b:=sigma(j)*sigma(a); if b>t then t:=b; fi;
  od;
  print(t);
od; end:
A211217(1000);

Mathematica

a[n_] := Max[Times @@ DivisorSigma[1, #]& /@ IntegerPartitions[n, {2}]]; Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Dec 26 2013 *)