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.

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

Offset: 0

Author

Rainer Rosenthal, Jul 07 2023

Keywords

• nonn

Comments

Number of occurrences of n in A077773.

Examples

			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.
		

Links

• Rainer Rosenthal, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A077773, A363761, A363762, A363763.

Programs

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