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

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Mar 19 2003

Keywords

• nonn

Examples

			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.
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..10000
• Ivars Peterson, Medieval Harmony.
• Eric Weisstein's World of Mathematics, Smooth Number.

Crossrefs

Cf. A081329, A081330, A081327, A081328, A003586.

Programs

Mathematica

nmax = 10000;
S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
P[n_] := IntegerPartitions[n, {2}, TakeWhile[S, # < n &] ];
a[n_] := P[n] // Length;
Array[a, nmax] (* Jean-François Alcover, Oct 13 2021 *)