OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
EXAMPLE
a(0) = 1: 0 = the empty sum.
a(1) = 1: 1 = 1*1.
a(4) = 2: 4 = 1*4 = 2*2.
a(5) = 2: 5 = 1*1 + 2*2 = 1*5.
a(9) = 3: 9 = 1*1 + 2*4 = 1*9 = 3*3.
a(12) = 4: 12 = 1*2 + 2*5 = 1*12 = 2*6 = 3*4.
a(15) = 5: 15 = 1*3 + 2*6 = 1*3 + 3*4 = 1*1 + 2*7 = 1*15 = 3*5.
MAPLE
with(numtheory):
b:= proc(n, m, i, j) option remember;
`if`(n=0, 1, `if`(m<1, 0, b(n, m-1, i, j) +`if`(m>n, 0,
add(b(n-m, m-1, min(i, k-1), min(j, m/k-1)), k=select(x->
is(x<=min(sqrt(m), i) and m<=j*x), divisors(m))))))
end:
a:= n-> b(n$4):
seq(a(n), n=0..30);
MATHEMATICA
b[n_, m_, i_, j_] := b[n, m, i, j] = If[n == 0, 1, If[m<1, 0, b[n, m-1, i, j]+If[m>n, 0, Sum[b[n-m, m-1, Min[i, k-1], Min[j, m/k-1]], {k, Select[Divisors[m], # <= Min[Sqrt[m], i] && m <= j*#&]}]]]]; a[n_] := b[n, n, n, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Dec 05 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 06 2012
STATUS
approved