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 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. 3
 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, 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, 1, 3, 3, 0, 5, 1, 4, 1, 2, 1, 3, 4, 0, 3, 3, 2, 2, 4, 0, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of occurrences of n in A077773. LINKS Rainer Rosenthal, Table of n, a(n) for n = 0..10000 EXAMPLE a(0) = 1, since A077773(k) = 0 at the single index k = 0. a(6) = 3, since A077773(k) = 6 for these 3 indices: k = 8, 9, and 11. a(46) = 0, since A077773 doesn't contain 46; see A363761, A363762 and A363763. PROG (Python) from sympy import factorint def A363522(n): s = 0 for k in range(n>>1, ((n+1)**2<<1)+1): c = 0 for m in range(k**2+1, (k+1)**2): if all(p==2 or p&3==1 or e&1^1 for p, e in factorint(m).items()): c += 1 if c>n: break if c==n: s += 1 return s # Chai Wah Wu, Jul 10 2023 CROSSREFS Cf. A077773, A363761, A363762, A363763. Sequence in context: A161506 A066451 A328048 * A091090 A305052 A305079 Adjacent sequences: A363519 A363520 A363521 * A363523 A363524 A363525 KEYWORD nonn AUTHOR Rainer Rosenthal, Jul 07 2023 STATUS approved

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Last modified February 21 06:16 EST 2024. Contains 370219 sequences. (Running on oeis4.)