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A081310 Numbers having no representation as sum of a prime and an 3-smooth number.

%I A081310 #13 Oct 13 2021 10:20:33
%S A081310 1,2,36,78,96,120,126,144,156,162,186,204,210,216,222,276,288,300,306,
%T A081310 324,328,330,336,342,366,372,378,396,408,414,426,438,456,474,486,498,
%U A081310 516,528,534,540,546,552,562,576,582,606,612,624,630,636,666,672,690
%N A081310 Numbers having no representation as sum of a prime and an 3-smooth number.
%C A081310 Complement of A081311.
%H A081310 Reinhard Zumkeller, <a href="/A081310/b081310.txt">Table of n, a(n) for n = 1..10000</a>
%F A081310 A081308(a(n)) = 0.
%e A081310 For all primes p<36 the greatest prime factor of 36-p is >3: 36-2=2*17, 36-3=3*11, 36-5=31, 36-7=29, 36-11=5*5, 36-13=23, 36-17=19, 36-19=17, 36-23=13, 36-29=7, 36-31=5, therefore 36 is a term.
%t A081310 nmax = 1000;
%t A081310 S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
%t A081310 A081308[n_] := Count[TakeWhile[S, # < n &], s_ /; PrimeQ[n - s]];
%t A081310 Select[Range[nmax], A081308[#] == 0 &] (* _Jean-François Alcover_, Oct 13 2021 *)
%o A081310 (Haskell)
%o A081310 a081310 n = a081310_list !! (n-1)
%o A081310 a081310_list = filter ((== 0) . a081308) [1..]
%o A081310 -- _Reinhard Zumkeller_, Jul 04 2012
%Y A081310 Cf. A000040, A003586, A081308, A081311.
%K A081310 nonn
%O A081310 1,2
%A A081310 _Reinhard Zumkeller_, Mar 17 2003