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%I #16 Sep 08 2022 08:46:21
%S 0,2,5,3,9,19,16,22,48,37,44,89,55,80,188,76,100,220,124,191,382,199,
%T 223,419,326,296,561,373,368,983,400,435,1001,514,872,1145,630,689,
%U 1483,956,794,1981,926,1075,2624,1085,1122,2340,1442,1700
%N Number of ways to express n^3 as average of two primes p1 < p2.
%H Hugo Pfoertner, <a href="/A305126/b305126.txt">Table of n, a(n) for n = 1..500</a>
%F a(n) = A002375(n^3).
%t f[n_]:=Length[Select[2 n - Prime[Range[2, PrimePi[n]]], PrimeQ]]; Table[f[n^3], {n, 60}] (* _Vincenzo Librandi_, May 26 2018 *)
%o (PARI) for (n=1,50,k=0;n3=2*n^3;forprime(p=3,n3/2,if(isprime(n3-p),k++));print1(k,", "))
%o (Magma) A305126 := func<n|#[p:p in[3..n]|IsPrime(p)and IsPrime(2*n-p)]>; [A305126(n^3):n in[1..70]]; // _Vincenzo Librandi_, May 26 2018
%Y Cf. A002375, A305125.
%K nonn
%O 1,2
%A _Hugo Pfoertner_, May 26 2018
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