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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
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
Sequence in context: A161506 A066451 A328048 * A091090 A305052 A305079
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.)