cp's OEIS Frontend

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

%I A117086 #19 Sep 03 2017 17:20:46
%S A117086 1,2,3,5,6,11,12,20,26,37,45,71,84,117,152,203,253,342,421,556,694,
%T A117086 884,1096,1409,1729,2168,2672,3327,4061,5039,6114,7514,9110,11098,
%U A117086 13400,16275,19537,23575,28245,33929,40465,48424,57552,68569,81296,96449
%N A117086 Number of partitions of n such that the largest part is a multiple of the smallest part.
%C A117086 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
%H A117086 Alois P. Heinz, <a href="/A117086/b117086.txt">Table of n, a(n) for n = 1..1000</a>
%F A117086 G.f.: Sum_{L>=0} Sum_{k>=1} (x^((L+1)*k) / Product_{i=k..L*k} (1 - x^i)).
%e A117086 a(7)=12 because from the 15 (=A000041(7)) partitions of 7 only [5,2],[4,3] and [3,2,2] do not qualify.
%p A117086 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
%t A117086 Table[Count[IntegerPartitions[n],_?(Divisible[First[#],Last[#]]&)], {n,50}] (* _Harvey P. Dale_, Mar 04 2012 *)
%Y A117086 Cf. A118096.
%Y A117086 Cf. A000041.
%K A117086 easy,nonn
%O A117086 1,2
%A A117086 _Vladeta Jovovic_, Apr 17 2006
%E A117086 More terms from _Emeric Deutsch_, Apr 21 2006