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A211218 Maximum value of sigma(x) + sigma(y) + sigma(z), where x + y + z = n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

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

LINKS

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

EXAMPLE

a(76) = sigma(4)+sigma(12)+sigma(60) = 7 + 28 + 168 = 203.

a(83) = sigma(1)+sigma(10)+sigma(72) = 1 + 18 + 195 = 214.

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-Fran├žois Alcover, Dec 26 2013 *)

PROG

(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

CROSSREFS

Cf. A085884, A211217, A211219.

Sequence in context: A195179 A033038 A195167 * A291839 A134917 A066665

Adjacent sequences:  A211215 A211216 A211217 * A211219 A211220 A211221

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Apr 05 2012

EXTENSIONS

Rewritten by R. J. Mathar, Apr 05 2012

STATUS

approved

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)