A085884 - OEIS

%I #13 Dec 26 2013 08:45:19

%S 2,4,6,8,10,13,15,16,19,19,24,29,31,32,35,34,40,40,43,43,46,46,56,61,

%T 63,64,67,66,72,73,75,76,79,78,88,92,94,95,98,97,103,99,106,104,109,

%U 103,120,125,127,128,131,130,136,132,139,137,142,136,152,169,171,172,175

%N Let r and s be such that r + s = n; a(n) = maximum value of sigma(r) + sigma(s).

%H Charles R Greathouse IV, <a href="/A085884/b085884.txt">Table of n, a(n) for n = 2..10000</a>

%e a(8) = 6, the partitions are ( 1,7),(2,6),(3,5),(4,4) which give 9, 15,10,14 as the sum of the sigma function of both the parts.

%t a[n_] := Max[Total[DivisorSigma[1, #]]& /@ IntegerPartitions[n, {2}]]; Table[a[n], {n, 2, 100}] (* _Jean-François Alcover_, Dec 26 2013 *)

%o (PARI) a(n)=my(best=sigma(n-1)+1);for(k=2,n\2,best=max(best, sigma(k)+sigma(n-k)));best \\ _Charles R Greathouse IV_, Apr 06 2012

%Y Cf. A085883.

%K nonn

%O 2,1

%A _Amarnath Murthy_, Jul 08 2003

%E More terms from _David Wasserman_, Feb 10 2005