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

0,3

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