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A384064 a(n) = s(n) divided by the smallest multiple prime factor of s(n), where s = A013929.

%I A384064 #26 Jun 25 2025 14:39:23
%S A384064 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,
%T A384064 36,15,38,40,27,42,44,30,46,48,14,33,50,52,54,56,58,39,60,11,62,25,42,
%U A384064 64,66,45,68,70,72,21,74,30,76,51,78,80,54,82,84,13,57,86
%N A384064 a(n) = s(n) divided by the smallest multiple prime factor of s(n), where s = A013929.
%C A384064 a(n) is the largest proper nonunitary divisor of s(n).
%H A384064 Michael De Vlieger, <a href="/A384064/b384064.txt">Table of n, a(n) for n = 1..10000</a>
%H A384064 Michael De Vlieger, <a href="/A384064/a384064.png">Log log scatterplot of a(n)</a>, 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.
%F A384064 a(n) = A013929(n)/A046027(n).
%t A384064 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]]
%o A384064 (Python)
%o A384064 from math import isqrt
%o A384064 from sympy import mobius, factorint
%o A384064 def A384064(n):
%o A384064     def f(x): return n+sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
%o A384064     m, k = n, f(n)
%o A384064     while m != k:
%o A384064         m, k = k, f(k)
%o A384064     s = factorint(m)
%o A384064     return m//next(p for p in sorted(s) if s[p]>1) # _Chai Wah Wu_, Jun 25 2025
%Y A384064 Cf. A013929, A046027, A048105.
%K A384064 nonn,easy
%O A384064 1,1
%A A384064 _Michael De Vlieger_, Jun 23 2025