OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..9000
FORMULA
G.f.: Sum(n*x^n/(1-x^n)*Product(1/(1-x^k), k = n .. infinity), n = 1 .. infinity).
a(n) ~ sqrt(2) * exp(Pi*sqrt(2*n/3)) / (4*Pi*sqrt(n)). - Vaclav Kotesovec, Jul 06 2019
EXAMPLE
Partitions of 4 are: [1,1,1,1], [1,1,2], [2,2], [1,3], [4]; thus a(4)=4*1+2*1+2*2+1*1+1*4=15.
MAPLE
b:= proc(n, i) option remember; `if`(irem(n, i)=0, n, 0)
+`if`(i>1, add(b(n-i*j, i-1), j=0..(n-1)/i), 0)
end:
a:= n-> b(n$2):
seq(a(n), n=1..50); # Alois P. Heinz, Feb 04 2016
MATHEMATICA
ss[n_]:=Module[{m=Min[n]}, Select[n, #==m&]]; Table[Total[Flatten[ss/@ IntegerPartitions[n]]], {n, 50}] (* Harvey P. Dale, Dec 16 2013 *)
b[n_, i_] := b[n, i] = If[Mod[n, i] == 0, n, 0] + If[i > 1, Sum[b[n - i*j, i - 1], {j, 0, (n - 1)/i}], 0]; a[n_] := b[n, n]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Aug 29 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Feb 16 2004
EXTENSIONS
More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
STATUS
approved