%I #15 Aug 05 2023 21:34:26
%S 87,159,183,199,204,207,231,247,252,303,319,324,327,343,348,351,364,
%T 367,372,399,423,439,444,463,468,471,484,487,492,495,511,516,532,535,
%U 540,543,556,559,564,567,583,588,591,604,607,612,628,655,660,663,676,679,684,700,703,708
%N Numbers which are the sum of 4 squares of distinct primes.
%H David A. Corneth, <a href="/A363281/b363281.txt">Table of n, a(n) for n = 1..10000</a>
%e 87 is a term as 87 = 2^2 + 3^2 + 5^2 + 7^2.
%t Select[Range@1000,
%t Length[PowersRepresentations[#, 4, 2] // Select[AllTrue@PrimeQ] //
%t Select[DuplicateFreeQ]] > 0 &]
%o (Python）
%o from itertools import combinations as comb
%o ps=[p**2 for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]]
%o a=[n for n in range(1001) if n in [sum(n) for n in list(comb(ps,4))]]
%o print(a)
%o (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
%Y Cf. A133524, A051395.
%K easy,nonn
%O 1,1
%A _Zhining Yang_, May 25 2023
