cp's OEIS Frontend

A363522 Number of integers k such that there are exactly n distinct numbers j with k^2 < j < (k+1)^2 which can be expressed as sum of two squares.

%I A363522 #36 Jul 10 2023 12:13:24
%S A363522 1,1,2,1,2,1,3,1,2,1,2,3,2,1,1,3,2,2,1,3,3,1,3,1,2,1,4,2,1,3,1,3,1,3,
%T A363522 1,4,1,3,2,1,1,4,1,4,2,3,0,2,3,3,3,2,2,2,1,0,3,5,1,4,1,4,0,2,2,3,4,1,
%U A363522 1,3,3,0,5,1,4,1,2,1,3,4,0,3,3,2,2,4,0,3
%N A363522 Number of integers k such that there are exactly n distinct numbers j with k^2 < j < (k+1)^2 which can be expressed as sum of two squares.
%C A363522 Number of occurrences of n in A077773.
%H A363522 Rainer Rosenthal, <a href="/A363522/b363522.txt">Table of n, a(n) for n = 0..10000</a>
%e A363522 a(0) = 1, since A077773(k) = 0 at the single index k = 0.
%e A363522 a(6) = 3, since A077773(k) = 6 for these 3 indices: k = 8, 9, and 11.
%e A363522 a(46) = 0, since A077773 doesn't contain 46; see A363761, A363762 and A363763.
%o A363522 (Python)
%o A363522 from sympy import factorint
%o A363522 def A363522(n):
%o A363522     s = 0
%o A363522     for k in range(n>>1,((n+1)**2<<1)+1):
%o A363522         c = 0
%o A363522         for m in range(k**2+1,(k+1)**2):
%o A363522             if all(p==2 or p&3==1 or e&1^1 for p, e in factorint(m).items()):
%o A363522                 c += 1
%o A363522                 if c>n:
%o A363522                     break
%o A363522         if c==n:
%o A363522             s += 1
%o A363522     return s # _Chai Wah Wu_, Jul 10 2023
%Y A363522 Cf. A077773, A363761, A363762, A363763.
%K A363522 nonn
%O A363522 0,3
%A A363522 _Rainer Rosenthal_, Jul 07 2023