A260375
Numbers k such that A260374(k) is a perfect square.
Original entry on oeis.org
0, 1, 2, 4, 5, 6, 7, 8, 10, 11, 14, 15, 16
Offset: 1
6! = 720. The nearest perfect square is 729. The difference is 9, which is itself a perfect square. So, 6 is in this sequence.
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is(n)=my(N=n!,s=sqrtint(N)); issquare(min(N-s^2, (s+1)^2-N)) \\ Charles R Greathouse IV, Jul 23 2015
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from gmpy2 import isqrt, is_square
A260375_list, g = [0], 1
for i in range(1, 1001):
g *= i
s = isqrt(g)
t = g-s**2
if is_square(t if t-s <= 0 else 2*s+1-t):
A260375_list.append(i) # Chai Wah Wu, Jul 23 2015
A260373
The nearest perfect square to n!
Original entry on oeis.org
1, 1, 1, 4, 25, 121, 729, 5041, 40401, 362404, 3629025, 39917124, 478996996, 6226945921, 87178467600, 1307674583296, 20922793332736, 355687416544329, 6402373660047556, 121645100663836929, 2432902009335560361, 51090942169052381124, 1124000727752683686724
Offset: 0
6! = 720. The nearest perfect square is 729.
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a(n)=round(sqrt(n!))^2 \\ Charles R Greathouse IV, Jul 23 2015
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from gmpy2 import isqrt
A260373_list, g = [1], 1
for i in range(1, 101):
g *= i
s = isqrt(g)
t = s**2
A260373_list.append(int(t if g-t-s <= 0 else t+2*s+1)) # Chai Wah Wu, Jul 23 2015
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