OFFSET
0,9
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: Product_{k>=1} (1 - mu(k)^2*x^k)/(1 - x^k), where mu(k) is the Moebius function (A008683). - Ilya Gutkovskiy, Dec 30 2016
EXAMPLE
a(12) = #{2*2*3, 2*2*2 + 2*2, 2*2 + 2*2 + 2*2} = 3;
a(13) = #{3*3 + 2*2} = 1.
MAPLE
with(numtheory):
b:= proc(n, i) option remember;
`if`(n=0, 1, `if`(i<1, 0, b(n, i-1)+
`if`(i>n or issqrfree(i), 0, b(n-i, i))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..100); # Alois P. Heinz, Jun 03 2015
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n || SquareFreeQ[i], 0, b[n-i, i]]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 30 2015, after Alois P. Heinz *)
PROG
(Haskell)
a114374 = p a013929_list where
p _ 0 = 1
p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Jun 01 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 09 2006
EXTENSIONS
Offset changed and a(0)=1 prepended by Reinhard Zumkeller, Jun 01 2015
STATUS
approved