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
Keywords
Examples
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.
Crossrefs
Cf. A113309.
Programs
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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 *)
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
Comments