A113308 a(n) = the number of finite sequences of positive integers {b(k)} where (product b(k))* (sum b(k)) = n. Different orderings of the same integers are counted separately.

1, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 8, 1, 7, 4, 10, 1, 13, 1, 15, 6, 11, 1, 27, 2, 13, 8, 28, 1, 27, 1, 36, 10, 17, 4, 62, 1, 19, 12, 59, 1, 47, 1, 66, 19, 23, 1, 118, 2, 31, 16, 91, 1, 78, 8, 117, 18, 29, 1, 193, 1, 31, 26, 159, 10, 115, 1, 153, 22, 51, 1, 320, 1, 37, 35, 190, 6, 161, 1

Offset

1,4

Comments

Sequence's terms calculated by "Max".

Links

Table of n, a(n) for n=1..79.

Formula

a(n)=1 if n=1 or is a prime, a(2)=2 if n is the square of a prime. - Robert G. Wilson v

Example

6 = 1*1*1*1*1*1*(1+1+1+1+1+1) = 1*2*(1+2) = 2*1*(2+1). So a(6) = 3.

Mathematica

(* first do *) Needs["DiscreteMath`Combinatorica`"] ( then *) t = Table[1, {80}]; Do[k = 1; lmt = PartitionsP@n; p = Partitions@n; While[k < lmt, a = Plus @@ p[[k]]*Times @@ p[[k]]; If[a < 81, t[[a]] += Length@ Permutations@ p[[k]]]; k++ ], {n, 40}]; t (* Robert G. Wilson v, May 03 2006 *)

Crossrefs

Cf. A113309.

Sequence in context: A361735 A064576 A322390 * A325332 A358195 A143862

Adjacent sequences: A113305 A113306 A113307 * A113309 A113310 A113311

Keyword

nonn

Author

Leroy Quet, Oct 25 2005

Status

approved