A085884 Let r and s be such that r + s = n; a(n) = maximum value of sigma(r) + sigma(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, 63, 64, 67, 66, 72, 73, 75, 76, 79, 78, 88, 92, 94, 95, 98, 97, 103, 99, 106, 104, 109, 103, 120, 125, 127, 128, 131, 130, 136, 132, 139, 137, 142, 136, 152, 169, 171, 172, 175

Offset: 2

Author

Amarnath Murthy, Jul 08 2003

Keywords

• nonn

Examples

			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.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A085883.

Programs

Mathematica

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

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

Extensions

More terms from David Wasserman, Feb 10 2005