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A261887 Number of triples of primes (p,q,r) that satisfy p+q^2+r^3=n.

%I A261887 #12 Oct 19 2024 15:57:32
%S A261887 0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,2,1,0,1,1,1,1,0,0,1,1,1,1,0,1,2,
%T A261887 2,3,0,3,1,2,2,1,2,2,0,2,1,2,2,2,0,1,2,3,3,1,1,1,4,3,0,3,1,3,3,0,1,2,
%U A261887 1,3,2,1,2,3,1,3,1,3,3,2,2,0,4,2,1,2,1,2,3,2
%N A261887 Number of triples of primes (p,q,r) that satisfy p+q^2+r^3=n.
%H A261887 Ana Rechtman, <a href="http://images-archive.math.cnrs.fr/Aout-2015-4eme-defi.html">Août 2015, 4e défi</a>, Images des Mathématiques, CNRS, 2015.
%F A261887 G.f.: (Sum_{i>=1} x^prime(i))*(Sum_{j>=1} x^(prime(j)^2))*(Sum_{k>=1} x^(prime(k)^3)). - _Ilya Gutkovskiy_, Feb 06 2017
%e A261887 For p=2, p+p^2+p^3 = 14 = A181149(1), so a(14)=1.
%o A261887 (PARI) a(n) = {nb = 0; forprime(p=2, n, forprime(q=2, n, if (p+q^2 > n, break); forprime(r=2, n, if (p+q^2+r^3 > n, break); if (p+q^2+r^3 == n, nb++);););); nb;}
%Y A261887 Cf. A181149 (p+p^2+p^3 with p prime), A261888.
%K A261887 nonn
%O A261887 1,19
%A A261887 _Michel Marcus_, Sep 05 2015