A363281 Numbers which are the sum of 4 squares of distinct primes.

87, 159, 183, 199, 204, 207, 231, 247, 252, 303, 319, 324, 327, 343, 348, 351, 364, 367, 372, 399, 423, 439, 444, 463, 468, 471, 484, 487, 492, 495, 511, 516, 532, 535, 540, 543, 556, 559, 564, 567, 583, 588, 591, 604, 607, 612, 628, 655, 660, 663, 676, 679, 684, 700, 703, 708

Offset: 1

Author

Zhining Yang, May 25 2023

Keywords

• easy
• nonn

Examples

			87 is a term as 87 = 2^2 + 3^2 + 5^2 + 7^2.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A133524, A051395.

Programs

Mathematica

Select[Range@1000,
 Length[PowersRepresentations[#, 4, 2] // Select[AllTrue@PrimeQ] //
     Select[DuplicateFreeQ]] > 0 &]

PARI

upto(n) = {if(n <= 86, return([])); my(pr = primes(primepi(sqrtint(n - 38))), res = List()); forvec(v = vector(4, i, [1, #pr]), c = sum(i = 1, #v, pr[v[i]]^2); if(c <= n, listput(res, c)), 2); listsort(res, 1); res} \\ David A. Corneth, Jul 12 2023

Python

from itertools import combinations as comb
ps=[p**2 for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]]
a=[n for n in range(1001) if n in [sum(n) for n in list(comb(ps,4))]]
print(a)