A081312 Numbers having a unique representation as sum of a prime and an 3-smooth number.

3, 24, 28, 42, 48, 52, 54, 58, 60, 66, 72, 90, 102, 108, 114, 132, 138, 150, 168, 172, 174, 180, 192, 196, 198, 214, 228, 234, 240, 246, 252, 264, 268, 270, 282, 294, 298, 312, 318, 348, 354, 360, 384, 390, 402, 404, 420, 432, 444, 450, 462, 468, 478, 480, 492

Offset: 1

Author

Reinhard Zumkeller, Mar 17 2003

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A003586, A081308, A081313.

Subsequence of A081311.

Programs

Haskell

a081312 n = a081312_list !! (n-1)
a081312_list = filter ((== 1) . a081308) [1..]
-- Reinhard Zumkeller, Jul 04 2012

Mathematica

sp3sQ[n_]:=Length[Select[IntegerPartitions[n,{2}],(PrimeQ[#[[1]]]&&Max[ FactorInteger[#[[2]]][[All,1]]]<4)||(PrimeQ[#[[2]]]&&Max[ FactorInteger[ #[[1]]][[All,1]]]<4)&]]==1; Select[Range[500],sp3sQ]/.(5->Nothing) (* Harvey P. Dale, Feb 05 2019 *)
nmax = 1000;
S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
A081308[n_] := Count[TakeWhile[S, # < n &], s_ /; PrimeQ[n - s]];
Select[Range[nmax], A081308[#] == 1 &] (* Jean-François Alcover, Oct 13 2021 *)

Formula

A081308(a(n)) = 1.