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%I #11 Oct 05 2017 13:25:03
%S 2,4,5,7,7,9,9,11,12,15,13,15,15,17,18,21,19,21,21,23,24,27,25,27,28,
%T 31,30,36,31,33,33,35,36,39,38,44,39,41,42,45,43,45,45,47,48,51,49,51,
%U 52,55,54,60,55,57,58,61,60,66,61,63,63,65,66,69,68,74,69,71,72,75,73,75
%N Let r and s be such that r + s = n; a(n) = minimum value of sigma(r) + sigma(s).
%C a(p+1) = p+2 if p is a prime.
%H Charles R Greathouse IV, <a href="/A085888/b085888.txt">Table of n, a(n) for n = 2..10000</a>
%e a(8) = 9: the partitions are ( 1,7),(2,6),(3,5),(4,4) which give 9,15,10,14 as the sum of sigma functions of both the parts.
%t Table[Min[Total[#]&/@(DivisorSigma[1,#]&/@({#,n-#}&/@Range[n/2]))],{n,2,80}] (* _Harvey P. Dale_, Oct 05 2017 *)
%o (PARI) a(n)=my(best=sigma(n-1)+1); for(k=2, n\2, best=min(best, sigma(k)+sigma(n-k))); best \\ _Charles R Greathouse IV_, Apr 06 2012
%Y Cf. A085884.
%K nonn
%O 2,1
%A _Amarnath Murthy_, Jul 08 2003
%E More terms from _David Wasserman_, Feb 10 2005
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