A305126 Number of ways to express n^3 as average of two primes p1 < p2.

0, 2, 5, 3, 9, 19, 16, 22, 48, 37, 44, 89, 55, 80, 188, 76, 100, 220, 124, 191, 382, 199, 223, 419, 326, 296, 561, 373, 368, 983, 400, 435, 1001, 514, 872, 1145, 630, 689, 1483, 956, 794, 1981, 926, 1075, 2624, 1085, 1122, 2340, 1442, 1700

Offset

1,2

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..500

Formula

a(n) = A002375(n^3).

Mathematica

f[n_]:=Length[Select[2 n - Prime[Range[2, PrimePi[n]]], PrimeQ]]; Table[f[n^3], {n, 60}] (* Vincenzo Librandi, May 26 2018 *)

Prog

(PARI) for (n=1, 50, k=0; n3=2*n^3; forprime(p=3, n3/2, if(isprime(n3-p), k++)); print1(k, ", "))
(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

Crossrefs

Cf. A002375, A305125.

Sequence in context: A193972 A361398 A332357 * A044043 A133128 A057337

Adjacent sequences: A305123 A305124 A305125 * A305127 A305128 A305129

Keyword

nonn

Author

Hugo Pfoertner, May 26 2018

Status

approved