A081332 Numbers having a unique partition into two 3-smooth numbers.

2, 3, 29, 31, 37, 41, 43, 49, 55, 58, 59, 62, 65, 67, 74, 83, 85, 86, 87, 89, 91, 93, 98, 109, 110, 111, 113, 116, 118, 123, 124, 130, 131, 134, 137, 147, 148, 155, 163, 165, 166, 170, 172, 174, 177, 178, 182, 186, 193, 195, 196, 201, 209, 217, 218, 220, 222, 226

Offset: 1

Author

Reinhard Zumkeller, Mar 19 2003

Keywords

• nonn

Crossrefs

Cf. A003586, A081326, A081333, A081330.

Programs

Mathematica

nmax = 1000;
S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
P[n_] := IntegerPartitions[n, {2}, TakeWhile[S, # < n &]];
selQ[n_] := Length[P[n]] == 1;
Select[Range[nmax], selQ] (* Jean-François Alcover, Oct 14 2021 *)

Formula

A081326(a(n)) = 1.