OFFSET
1,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum(q(k)), where k divides n, k < n, where q(n) = A000009(n), distinct partitions. - Alford Arnold
EXAMPLE
E.g. 6 = 1+1+1+1+1+1 = 2+2+2 = 3+3 = 2+1+2+1, so a(6)=4.
MAPLE
with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1, add(add(
`if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)
end:
a:= n-> add(b(d), d=divisors(n) minus {n}):
seq(a(n), n=1..100); # Alois P. Heinz, Jul 11 2016
MATHEMATICA
b[n_] := b[n] = If[n == 0, 1, Sum[Sum[If[OddQ[d], d, 0], {d, Divisors[j]}]* b[n-j], {j, 1, n}]/n]; a[n_] := Sum[b[d], {d, Divisors[n] ~Complement~ {n}}]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 25 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(1) set to 0 by Alois P. Heinz, Jul 11 2016
STATUS
approved