OFFSET
0,3
LINKS
Hugo Pfoertner, Table of n, a(n) for n = 0..3000
FORMULA
If a(n) != -1, then a(n) >= n/2. - Chai Wah Wu, Jun 22 2023
a(n) = A363763(n) for n <= 11459.
a(n) = -1 for n > 15898.
PROG
(PARI) a363761(upto) = {for (n=0, upto, my(kfound=-1);
for (k=0, 3*n, my(k1=k^2+1, k2=k*(k+2), m=0);
for (j=k1, k2, m+= (sumdiv(j, d, (d%4==1)-(d%4==3))>0); if (m>n, break));
if (m==n, kfound=k; break); if (m==n, kfound=k; break)); print1(kfound, ", "))};
a363761(75)
(Python)
from sympy import factorint
def A363761(n):
for k in range(n>>1, 3*n):
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:
return k
return -1 # Chai Wah Wu, Jun 22 2023
CROSSREFS
KEYWORD
sign
AUTHOR
Hugo Pfoertner, Jun 22 2023
STATUS
approved