OFFSET
0,2
COMMENTS
a(n) is the least k such that GCD(sopf(k), Omega(k)) = n. We assume that GCD(0,0) = 0.
EXAMPLE
The least k such that GCD(sopf(k), Omega(k)) = 0 is k = 1, thus a(0) = 1.
The least k such that GCD(sopf(k), Omega(k)) = 1 is k = 2, thus a(1) = 2.
The least k such that GCD(sopf(k), Omega(k)) = 2 is k = 4, thus a(2) = 4.
PROG
(Python)
from sympy import factorint
from math import gcd
def a(n, search_limit=10**5) -> int:
for k in range(1, search_limit):
f = factorint(k)
if n == gcd(sum(f.keys()), sum(f.values())):
return k
# if no k was found within the search range
return -1
print([a(n) for n in range(14)]) # Peter Luschny, Nov 02 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Oct 30 2025
STATUS
approved
