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A046027 Smallest multiple prime factor of the n-th nonsquarefree number (A013929).

%I A046027 #29 Jun 24 2025 05:23:04
%S A046027 2,2,3,2,2,3,2,2,5,3,2,2,2,2,2,3,2,7,5,2,3,2,2,3,2,2,2,5,2,2,3,2,2,3,
%T A046027 2,2,7,3,2,2,2,2,2,3,2,11,2,5,3,2,2,3,2,2,2,7,2,5,2,3,2,2,3,2,2,13,3,
%U A046027 2,5,2,2,2,2,3,2,2,3,2,2,3,2,2,2,2,2,3,2,2,3,2,2,11,3,2,7,2,5,2,2,2,3
%N A046027 Smallest multiple prime factor of the n-th nonsquarefree number (A013929).
%H A046027 Amiram Eldar, <a href="/A046027/b046027.txt">Table of n, a(n) for n = 1..10000</a>
%H A046027 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LeastPrimeFactor.html">Least Prime Factor</a>.
%H A046027 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squareful.html">Squareful</a>.
%F A046027 a(n) = A249739(A013929(n)). - _Amiram Eldar_, Feb 11 2021
%t A046027 Select[ FactorInteger[#], #[[2]]>1&, 1][[1, 1]]& /@ Select[ Range[300], !SquareFreeQ[#]& ] (* _Jean-François Alcover_, Nov 06 2012 *)
%o A046027 (Python)
%o A046027 from math import isqrt
%o A046027 from sympy import mobius, factorint
%o A046027 def A046027(n):
%o A046027     def f(x): return n+sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
%o A046027     m, k = n, f(n)
%o A046027     while m != k:
%o A046027         m, k = k, f(k)
%o A046027     s = factorint(m)
%o A046027     return next(p for p in sorted(s) if s[p]>1) # _Chai Wah Wu_, Jul 22 2024
%o A046027 (PARI) lista(nn) = apply(x->factor(x)[1,1], apply(x->x/core(x), select(x->!issquarefree(x), [1..nn]))); \\ _Michel Marcus_, Jun 24 2025
%Y A046027 Cf. A013929, A020639, A046028, A249739.
%K A046027 nonn
%O A046027 1,1
%A A046027 _Eric W. Weisstein_