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

1,4

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.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A122921 A174273 A108128 * A277879 A257071 A332025

Adjacent sequences: A081323 A081324 A081325 * A081327 A081328 A081329

Keyword

nonn

Author

Reinhard Zumkeller, Mar 19 2003

Status

approved