cp's OEIS Frontend

A045698 Number of ways n can be written as the sum of two squares of primes.

%I A045698 #27 Jan 09 2023 07:41:37
%S A045698 0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
%T A045698 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
%U A045698 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0
%N A045698 Number of ways n can be written as the sum of two squares of primes.
%C A045698 a(A214879(n)) = 0; a(A045636(n)) > 0; a(A214723(n)) = 1; a(A214511(n)) = n and a(m) < n for m < A214511(n). - _Reinhard Zumkeller_, Jul 29 2012
%C A045698 The smallest value of n such that a(n) = 2 is 338. (This helps distinguish it from the characteristic function of A045636.) - _Wesley Ivan Hurt_, Jun 13 2013
%H A045698 Reinhard Zumkeller, <a href="/A045698/b045698.txt">Table of n, a(n) for n = 0..10000</a>
%H A045698 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e A045698 For example, a(29) = 1 because 29 = 2^2 + 5^2. a(3) = 0 because there is no way to write 3 as sum of two squares of primes.
%o A045698 (Haskell)
%o A045698 a045698 n = length $ filter (\x -> x > 0 && a010051' x == 1) $
%o A045698 map (a037213 . (n -)) $
%o A045698 takeWhile (<= div n 2) a001248_list
%o A045698 -- _Reinhard Zumkeller_, Jul 29 2012
%o A045698 (PARI) a(n)=my(s=0,q);forprime(p=2,sqrtint(n\2),if(issquare(n-p^2,&q)&&isprime(q),s++));s \\ _Charles R Greathouse IV_, Jun 04 2014
%Y A045698 Cf. A001248, A010051, A037213.
%K A045698 easy,nonn
%O A045698 0,339
%A A045698 _Felice Russo_
%E A045698 More terms from _Erich Friedman_