A211218 Maximum value of sigma(x) + sigma(y) + sigma(z), where x + y + z = n.

3, 5, 7, 9, 11, 14, 16, 18, 20, 22, 25, 30, 32, 34, 36, 38, 41, 43, 44, 47, 47, 52, 57, 62, 64, 66, 68, 70, 73, 75, 76, 79, 80, 84, 89, 93, 95, 97, 99, 101, 104, 106, 107, 110, 110, 116, 121, 126, 128, 130, 132, 134, 137, 139, 140, 143

Offset: 3

Author

Paolo P. Lava, Apr 05 2012

Keywords

• nonn

Comments

Not monotonic: a(86) = 235 > 234 = a(87). - Charles R Greathouse IV, Apr 06 2012

Examples

			a(76) = sigma(4)+sigma(12)+sigma(60) = 7 + 28 + 168 = 203.
a(83) = sigma(1)+sigma(10)+sigma(72) = 1 + 18 + 195 = 214.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A085884, A211217, A211219.

Programs

Maple

with(numtheory) :
A211218 := proc(n)
        local x,y,z,mx ;
        mx := 0 ;
        for x from 1 to n do
                for y from x do
                        z := n-x-y ;
                        if z < y then
                                break;
                        end if;
                        mx := max(mx, sigma(x)+sigma(y)+sigma(z)) ;
                end do:
        end do:
        mx ;
end proc: # R. J. Mathar, Apr 05 2012

Mathematica

a[n_] := Max[Plus @@ DivisorSigma[1, #]& /@ IntegerPartitions[n, {3}]]; Table[a[n], {n, 3, 100}] (* Jean-François Alcover, Dec 26 2013 *)

PARI

v=vector(200);for(n=2,#v,best=sigma(n-1)+1;for(k=2,n\2, best=max(best,sigma(k)+sigma(n-k)));v[n]=best)
u=vector(#v);for(n=3,#u,best=sigma(n-2)+v[2];for(k=2,n-3, best=max(best,sigma(k)+v[n-k]));u[n]=best)
vecextract(u,"3..") \\ Charles R Greathouse IV, Apr 06 2012

Extensions

Rewritten by R. J. Mathar, Apr 05 2012