A305125 Number of ways to express n^2 as average of two primes p1 < p2.

0, 1, 2, 2, 4, 6, 3, 3, 10, 8, 8, 17, 9, 11, 27, 11, 12, 27, 14, 21, 39, 17, 19, 36, 28, 22, 48, 25, 24, 75, 30, 25, 68, 35, 56, 68, 37, 40, 93, 54, 43, 103, 42, 52, 125, 51, 49, 117, 64, 76, 130, 63, 56, 135, 99, 78, 151, 76, 73, 198

Offset: 1

Author

Hugo Pfoertner, May 26 2018

Keywords

• nonn
• look

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002375, A172989, A304874, A304875, A304903, A304904, A304905, A305126.

Programs

Mathematica

f[n_]:=Length[Select[2 n - Prime[Range[2, PrimePi[n]]], PrimeQ]]; Table[f[n^2], {n, 60}] (* Vincenzo Librandi, May 26 2018 *)

PARI

for (n=1,60,k=0;n2=2*n*n;forprime(p=3,n2/2,if(isprime(n2-p),k++));print1(k,", "))

Formula

a(n) = A002375(n^2).