A085888 Let r and s be such that r + s = n; a(n) = minimum value of sigma(r) + sigma(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, 31, 30, 36, 31, 33, 33, 35, 36, 39, 38, 44, 39, 41, 42, 45, 43, 45, 45, 47, 48, 51, 49, 51, 52, 55, 54, 60, 55, 57, 58, 61, 60, 66, 61, 63, 63, 65, 66, 69, 68, 74, 69, 71, 72, 75, 73, 75

Offset

2,1

Comments

a(p+1) = p+2 if p is a prime.

Links

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

Example

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.

Mathematica

Table[Min[Total[#]&/@(DivisorSigma[1, #]&/@({#, n-#}&/@Range[n/2]))], {n, 2, 80}] (* Harvey P. Dale, Oct 05 2017 *)

Prog

(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

Crossrefs

Cf. A085884.

Sequence in context: A288758 A210936 A140203 * A329531 A187325 A112233

Adjacent sequences: A085885 A085886 A085887 * A085889 A085890 A085891

Keyword

nonn

Author

Amarnath Murthy, Jul 08 2003

Extensions

More terms from David Wasserman, Feb 10 2005

Status

approved