A048261 - OEIS

%I #18 Mar 26 2022 10:20:00

%S 4,9,13,25,29,34,38,49,53,58,62,74,78,83,87,121,125,130,134,146,150,

%T 155,159,169,170,173,174,178,179,182,183,194,195,198,199,203,204,207,

%U 208,218,222,227,231,243,247,252,256,289,290,293,294,298,299,302,303

%N Numbers that are the sum of the squares of distinct primes.

%C 17163 is the largest of 2438 positive integers that can't be expressed as the sum of squares of distinct primes. See A121518. - _T. D. Noe_, Aug 04 2006

%D D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry 17163.

%H T. D. Noe, <a href="/A048261/b048261.txt">Table of n, a(n) for n = 1..2000</a>

%H Robert E. Dressler, Louis Pigno, and Robert Young, <a href="http://www.jstor.org/stable/43774462">Sums of squares of primes</a>, Nordisk Mat. Tidskr. 24 (1976), 39-40. MR 54 #7373.

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%F It is easy to check that these 2438 numbers that are not the sum of distinct primes squared are all of the form sum_i e_i*q_i where e_i is 1 or -1 and the q_i's are distinct primes. - _W. Edwin Clark_, Oct 19 2003

%e 13 = 2^2 + 3^2.

%t nn=10; s={0}; Do[p=Prime[n]; s=Union[s,s+p^2], {n,nn}]; s=Select[s,0<#<=Prime[nn]^2&] (* _T. D. Noe_, Aug 04 2006 *)

%Y Cf. A024450 (sum of squares of the first n primes).

%K nonn

%O 1,1

%A _Jud McCranie_