A117086 Number of partitions of n such that the largest part is a multiple of the smallest part.

1, 2, 3, 5, 6, 11, 12, 20, 26, 37, 45, 71, 84, 117, 152, 203, 253, 342, 421, 556, 694, 884, 1096, 1409, 1729, 2168, 2672, 3327, 4061, 5039, 6114, 7514, 9110, 11098, 13400, 16275, 19537, 23575, 28245, 33929, 40465, 48424, 57552, 68569, 81296, 96449

Offset: 1

Author

Vladeta Jovovic, Apr 17 2006

Keywords

• easy
• nonn

Comments

Also number of partitions of n such that the number of parts is a multiple of the multiplicity of the largest part. Example: a(7)=12 because from the 15 (=A000041(7)) partitions of 7 only [3,3,1], [2,2,2,1] and [2,2,1,1,1] do not qualify (3,4,5 are not multiples of 2,3,2, respectively). - Emeric Deutsch, Apr 21 2006

Examples

			a(7)=12 because from the 15 (=A000041(7)) partitions of 7 only [5,2],[4,3] and [3,2,2] do not qualify.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A118096.

Cf. A000041.

Programs

Maple

f:=add(add(x^((l+1)*k)/mul(1-x^i,i=k..l*k),k=1..51),l=0..51): s:=series(f,x,51):for m from 1 to 50 do c:=coeff(s,x,m): printf(`%d,`,c);od: # (Jovovic) - Emeric Deutsch, Apr 21 2006

Mathematica

Table[Count[IntegerPartitions[n],?(Divisible[First[#],Last[#]]&)], {n,50}] (* _Harvey P. Dale, Mar 04 2012 *)

Formula

G.f.: Sum_{L>=0} Sum_{k>=1} (x^((L+1)*k) / Product_{i=k..L*k} (1 - x^i)).

Extensions

More terms from Emeric Deutsch, Apr 21 2006