A389639 Number of ways to write 2*n as the sum of four (not necessarily distinct) squares of primes.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1

Offset

1,74

Comments

Numbers k such that 2*k can be represented as the sum of four (not necessarily distinct) squares of primes are in A389638.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Example

 16 = 2^2 + 2^2 + 2^2 + 2^2.
148 = 3^2 + 3^2 + 3^2 + 11^2 = 5^2 + 5^2 + 7^2 + 7^2.
196 = 3^2 + 3^2 + 3^2 + 13^2 = 5^2 + 5^2 + 5^2 + 11^2 = 7^2 + 7^2 + 7^2 + 7^2.

Mathematica

A389639list[pmax_] := With[{ps = Prime[Range[pmax + 1]]^2}, BinCounts[#, {1, Max[#], 1}] & [Select[Flatten[Table[ps[[i]] + ps[[j]] + ps[[k]] + ps[[l]], {i, pmax}, {j, i, pmax}, {k, j, pmax}, {l, k, pmax}]], IntegerQ[#/2] && # <= Last[ps] &]/2]];
A389639list[6] (* Paolo Xausa, Oct 25 2025 *)

Crossrefs

Cf. A389638, A389517, A001248, A002375, A002828.

Sequence in context: A134363 A054015 A375933 * A373976 A369164 A370815

Adjacent sequences: A389636 A389637 A389638 * A389640 A389641 A389642

Keyword

nonn

Author

Peter Luschny, Oct 09 2025

Status

approved