1,1

a(n) is the largest proper nonunitary divisor of s(n).

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^14, showing primes in red, proper prime powers in gold, squarefree composites in green, and numbers neither squarefree nor prime powers in blue and purple, where purple additionally signifies powerful numbers that are not prime powers.

a(n) = A013929(n)/A046027(n).

Map[#/Select[FactorInteger[#], #[[-1]] > 1 &, 1][[1, 1]] &, Select[Range[200], Not @* SquareFreeQ] ] (* or *) Map[Select[Most@ Divisors[#], Not @* CoprimeQ] &, Select[Range[200], Not @* SquareFreeQ] ][[All, -1]]

(Python)

from math import isqrt

from sympy import mobius, factorint

def A384064(n):

def f(x): return n+sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))

m, k = n, f(n)

while m != k:

m, k = k, f(k)

s = factorint(m)

return m//next(p for p in sorted(s) if s[p]>1) # Chai Wah Wu, Jun 25 2025

Cf. A013929, A046027, A048105.

Sequence in context: A364884 A369825 A382255 * A266411 A264740 A349370

Adjacent sequences: A384061 A384062 A384063 * A384065 A384066 A384067

nonn,easy

Michael De Vlieger, Jun 23 2025

approved