cp's OEIS Frontend

A238404 Number of ways a prime from A087054 can be decomposed as a sum of the form p*q+q*r+r*p where p, q and r are distinct primes (p < q < r).

%I A238404 #4 Feb 26 2014 11:32:49
%S A238404 1,1,1,1,2,2,1,1,2,3,3,4,1,2,1,1,1,1,3,2,2,1,1,8,1,1,2,3,2,1,1,3,2,1,
%T A238404 1,3,1,5,4,3,1,3,1,1,4,1,1,3,2,4,1,1,3,1,1,2,1,3,2,2,1,1,3,2,5,1,1,7,
%U A238404 8,1,3,4,1,6,3,2,12,1,1,1,1,5,2,1,9,1,1,1,2,1,5,1,2,1,3,3,1,2,7,1
%N A238404 Number of ways a prime from A087054 can be decomposed as a sum of the form p*q+q*r+r*p where p, q and r are distinct primes (p < q < r).
%e A238404 A087054(5) = 71 = 3*5 + 5*7 + 7*3 = 2*3 + 3*13 + 13*2, therefore a(5) = 2.
%t A238404 nn = 100; A087854 = Take[Select[ Union[Total[Times @@@ Subsets[#, {2}]] & /@ Subsets[Prime[Range[nn]], {3}]], PrimeQ], nn]; r[n_, p_] := Reduce[p < q < r && p*q+q*r+r*p == n, {q, r}, Primes]; a[n_] := (For[cnt = 0; p = 2, p <= Ceiling[(n-6)/5], p = NextPrime[p], rnp = r[n, p]; If[rnp =!= False, Which[rnp[[0]] === And, Print["n = ", n, " ", {p, q, r} /. ToRules[rnp]]; cnt++, rnp[[0]] === Or, Print["n = ", n, " ", {p, q, r} /. {ToRules[rnp]}]; cnt += Length[rnp], True, Print["error: n = ", n, " ", rnp]]]]; cnt); Reap[Do[ap = a[p]; If[ap > 0, Sow[ap]], {p, A087854}]][[2, 1]] (* after _Harvey P. Dale_ *)
%Y A238404 Cf. A087053, A087054.
%K A238404 nonn
%O A238404 1,5
%A A238404 _Jean-François Alcover_, Feb 26 2014