A085887 Let r and s be such that r + s = n; a(n) = minimum value of tau(r) + tau(s).

2, 3, 3, 4, 3, 4, 3, 4, 4, 5, 3, 4, 3, 4, 4, 5, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 6, 3, 4, 3, 4, 4, 5, 4, 6, 3, 4, 4, 5, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 6, 3, 4, 4, 5, 4, 5, 3, 4, 3, 4, 4, 5, 4, 6, 3, 4, 4, 5, 3, 4, 3, 4, 4, 5, 4, 6, 3, 4, 4, 5, 3, 4, 4, 5, 4, 6, 3, 4, 4, 5, 4, 5, 4, 6, 3, 4, 4, 5, 3, 4, 3, 4, 4

Offset

2,1

Comments

a(p+1) = 3 if p is a prime. a(n) = 4 if n is the sum of two primes. For all even numbers > 4, a(n) = 4 by Goldbach's conjecture.

Links

Antti Karttunen, Table of n, a(n) for n = 2..16385

Example

a(8) = 3, the partitions are (1,7), (2,6), (3,5), (4,4) which give 3, 6, 4 and 6 as the sum of the number of divisors of both parts.

Mathematica

Table[Min[Total/@DivisorSigma[0, IntegerPartitions[n, {2}]]], {n, 2, 120}] (* Harvey P. Dale, Mar 18 2023 *)

Prog

(PARI) A085887(n) = { my(m=0, k); for(r=1, n-1, if((m > k=(numdiv(r)+numdiv(n-r)))||!m, m = k)); m; }; \\ Antti Karttunen, Dec 14 2017

Crossrefs

Cf. A085883.

Sequence in context: A096344 A030349 A285203 * A305716 A297616 A213251

Adjacent sequences: A085884 A085885 A085886 * A085888 A085889 A085890

Keyword

nonn

Author

Amarnath Murthy, Jul 08 2003

Extensions

More terms from David Wasserman, Feb 10 2005

Status

approved