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URL: https://oeis.org/A384064

⇱ A384064 - OEIS


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A384064
a(n) = s(n) divided by the smallest multiple prime factor of s(n), where s = A013929.
1
2, 4, 3, 6, 8, 6, 10, 12, 5, 9, 14, 16, 18, 20, 22, 15, 24, 7, 10, 26, 18, 28, 30, 21, 32, 34, 36, 15, 38, 40, 27, 42, 44, 30, 46, 48, 14, 33, 50, 52, 54, 56, 58, 39, 60, 11, 62, 25, 42, 64, 66, 45, 68, 70, 72, 21, 74, 30, 76, 51, 78, 80, 54, 82, 84, 13, 57, 86
OFFSET
1,1
COMMENTS
a(n) is the largest proper nonunitary divisor of s(n).
LINKS
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.
FORMULA
a(n) = A013929(n)/A046027(n).
MATHEMATICA
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]]
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Jun 23 2025
STATUS
approved