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A081326 Number of partitions of n into two 3-smooth numbers.

%I A081326 #7 Feb 16 2025 08:32:48
%S A081326 0,1,1,2,2,2,2,2,2,3,2,3,2,2,2,2,2,3,2,3,2,2,0,3,2,2,2,3,1,3,1,2,3,2,
%T A081326 2,4,1,2,2,3,1,2,1,2,2,0,0,3,1,2,2,2,0,3,1,3,2,1,1,3,0,1,2,2,1,3,1,2,
%U A081326 0,2,0,4,2,1,2,2,0,2,0,3,2,2,1,3,1,1,1,2,1,3,1,0,1,0,0,3,2,1,3,2,0,2,0,2,2
%N A081326 Number of partitions of n into two 3-smooth numbers.
%H A081326 Jean-François Alcover, <a href="/A081326/b081326.txt">Table of n, a(n) for n = 1..10000</a>
%H A081326 Ivars Peterson, <a href="http://www.sciencenews.org/sn_arc99/1_23_99/mathland.htm">Medieval Harmony</a>.
%H A081326 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmoothNumber.html">Smooth Number</a>.
%e A081326 n=10 has a(10)=3 partitions into 3-smooth numbers: 10=1+3^2=2+2^3=2^2+2*3; n=9 has a(9)=2 partitions into 3-smooth numbers: 9=1+2^3=3+2*3.
%t A081326 nmax = 10000;
%t A081326 S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
%t A081326 P[n_] := IntegerPartitions[n, {2}, TakeWhile[S, # < n &] ];
%t A081326 a[n_] := P[n] // Length;
%t A081326 Array[a, nmax] (* _Jean-François Alcover_, Oct 13 2021 *)
%Y A081326 Cf. A081329, A081330, A081327, A081328, A003586.
%K A081326 nonn
%O A081326 1,4
%A A081326 _Reinhard Zumkeller_, Mar 19 2003