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

1,1

Links

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

Example

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

Mathematica

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

Prog

(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)
(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

Crossrefs

Cf. A133524, A051395.

Sequence in context: A095567 A205672 A039489 * A031891 A147140 A044257

Adjacent sequences: A363278 A363279 A363280 * A363282 A363283 A363284

Keyword

easy,nonn

Author

Zhining Yang, May 25 2023

Status

approved