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%I #15 Oct 13 2021 04:51:18
%S 3,24,28,42,48,52,54,58,60,66,72,90,102,108,114,132,138,150,168,172,
%T 174,180,192,196,198,214,228,234,240,246,252,264,268,270,282,294,298,
%U 312,318,348,354,360,384,390,402,404,420,432,444,450,462,468,478,480,492
%N Numbers having a unique representation as sum of a prime and an 3-smooth number.
%H Reinhard Zumkeller, <a href="/A081312/b081312.txt">Table of n, a(n) for n = 1..10000</a>
%F A081308(a(n)) = 1.
%t 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 *)
%t nmax = 1000;
%t S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
%t A081308[n_] := Count[TakeWhile[S, # < n &], s_ /; PrimeQ[n - s]];
%t Select[Range[nmax], A081308[#] == 1 &] (* _Jean-François Alcover_, Oct 13 2021 *)
%o (Haskell)
%o a081312 n = a081312_list !! (n-1)
%o a081312_list = filter ((== 1) . a081308) [1..]
%o -- _Reinhard Zumkeller_, Jul 04 2012
%Y Cf. A000040, A003586, A081308, A081313.
%Y Subsequence of A081311.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Mar 17 2003
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