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A081312
Numbers having a unique representation as sum of a prime and an 3-smooth number.
4
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
1,1
LINKS
FORMULA
A081308(a(n)) = 1.
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 *)
PROG
(Haskell)
a081312 n = a081312_list !! (n-1)
a081312_list = filter ((== 1) . a081308) [1..]
-- Reinhard Zumkeller, Jul 04 2012
CROSSREFS
Subsequence of A081311.
Sequence in context: A065430 A175471 A035409 * A123598 A106217 A267274
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 17 2003
STATUS
approved