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A211218
Maximum value of sigma(x) + sigma(y) + sigma(z), where x + y + z = n.
4
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
3,1
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-François 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
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Apr 05 2012
EXTENSIONS
Rewritten by R. J. Mathar, Apr 05 2012
STATUS
approved