A261887 - OEIS

%I #11 Jan 19 2019 04:14:59

%S 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 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 1,3,2,1,2,3,1,3,1,3,3,2,2,0,4,2,1,2,1,2,3,2

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

%H Ana Rechtman, <a href="http://images.math.cnrs.fr/Aout-2015-4eme-defi.html">Août 2015, 4e défi</a>, Images des Mathématiques, CNRS, 2015.

%F 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 For p=2, p+p^2+p^3 = 14 = A181149(1), so a(14)=1.

%o (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 Cf. A181149 (p+p^2+p^3 with p prime), A261888.

%K nonn

%O 1,19

%A _Michel Marcus_, Sep 05 2015