A125516 Prime numbers that are the sum of three distinct positive squares.
29, 41, 53, 59, 61, 83, 89, 101, 107, 109, 113, 131, 137, 139, 149, 157, 173, 179, 181, 197, 211, 227, 229, 233, 241, 251, 257, 269, 277, 281, 283, 293, 307, 313, 317, 331, 337, 347, 349, 353, 373, 379, 389, 397, 401, 409, 419, 421, 433, 443, 449, 457, 461
Offset: 1
Keywords
Examples
29 = 2^2 + 3^2 + 4^2 = 4 + 9 + 16. 89 = 2^2 + 6^2 + 7^2 = 4 + 36 + 49; also 89 = 3^2 + 4^2 + 8^2 = 9 + 16 + 64. 353 = 2^2 + 5^2 + 18^2 = 4 + 25 + 324; also 353 = 4^2 + 9^2 + 16^2 = 16 + 81 + 256.
Links
- Zak Seidov, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
Select[Total/@Subsets[Range[20]^2,{3}],PrimeQ]//Union (* Harvey P. Dale, Aug 12 2025 *) -
PARI
{m=22;p=m^2;v=vector(m,x,x^2);w=[];for(i=1,m-2,for(j=i+1,m-1,for(k=j+1,m,if((n=v[i]+v[j]+v[k])
Extensions
Edited, corrected and extended by Klaus Brockhaus, Feb 11 2007