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A046028 Largest multiple prime factor of the n-th nonsquarefree number (A013929).

%I A046028 #33 Feb 16 2025 08:32:38
%S A046028 2,2,3,2,2,3,2,2,5,3,2,2,3,2,2,3,2,7,5,2,3,2,2,3,2,2,3,5,2,2,3,2,2,3,
%T A046028 2,2,7,3,5,2,3,2,2,3,2,11,2,5,3,2,2,3,2,2,3,7,2,5,2,3,2,2,3,2,2,13,3,
%U A046028 2,5,2,3,2,2,3,2,7,3,5,2,3,2,2,3,2,2,5,2,2,3,2,2,11,3,2,7,2,5,3,2,2,3
%N A046028 Largest multiple prime factor of the n-th nonsquarefree number (A013929).
%H A046028 Reinhard Zumkeller, <a href="/A046028/b046028.txt">Table of n, a(n) for n = 1..10000</a>
%H A046028 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GreatestPrimeFactor.html">Greatest Prime Factor</a>.
%H A046028 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squareful.html">Squareful</a>.
%F A046028 a(n) = A249740(A013929(n)). - _Amiram Eldar_, Feb 11 2021
%t A046028 Select[ FactorInteger[#]//Reverse, #[[2]]>1&, 1][[1, 1]]& /@ Select[ Range[300], !SquareFreeQ[#]& ] (* _Jean-François Alcover_, Nov 06 2012 *)
%o A046028 (Haskell)
%o A046028 a046028 n = a046028_list !! (n-1)
%o A046028 a046028_list = f 1 where
%o A046028    f x | null zs   = f (x + 1)
%o A046028        | otherwise = (fst $ head zs) : f (x + 1)
%o A046028        where zs = reverse $ filter ((> 1) . snd) $
%o A046028                   zip (a027748_row x) (a124010_row x)
%o A046028 -- _Reinhard Zumkeller_, Dec 29 2012
%o A046028 (Python)
%o A046028 from math import isqrt
%o A046028 from sympy import mobius, factorint
%o A046028 def A046028(n):
%o A046028     def f(x): return n+sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
%o A046028     m, k = n, f(n)
%o A046028     while m != k:
%o A046028         m, k = k, f(k)
%o A046028     s = factorint(m)
%o A046028     return next(p for p in sorted(s,reverse=True) if s[p]>1) # _Chai Wah Wu_, Jul 22 2024
%Y A046028 Cf. A006530, A046027, A013929, A249740.
%Y A046028 Cf. A027748, A124010, A212177.
%K A046028 nonn,easy,nice
%O A046028 1,1
%A A046028 _Eric W. Weisstein_