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Largest multiple prime factor of the n-th nonsquarefree number (A013929).
4

%I #32 Jul 23 2024 10:53:36

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

%H Reinhard Zumkeller, <a href="/A046028/b046028.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GreatestPrimeFactor.html">Greatest Prime Factor</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squareful.html">Squareful</a>.

%F a(n) = A249740(A013929(n)). - _Amiram Eldar_, Feb 11 2021

%t Select[ FactorInteger[#]//Reverse, #[[2]]>1&, 1][[1, 1]]& /@ Select[ Range[300], !SquareFreeQ[#]& ] (* _Jean-François Alcover_, Nov 06 2012 *)

%o (Haskell)

%o a046028 n = a046028_list !! (n-1)

%o a046028_list = f 1 where

%o f x | null zs = f (x + 1)

%o | otherwise = (fst $ head zs) : f (x + 1)

%o where zs = reverse $ filter ((> 1) . snd) $

%o zip (a027748_row x) (a124010_row x)

%o -- _Reinhard Zumkeller_, Dec 29 2012

%o (Python)

%o from math import isqrt

%o from sympy import mobius, factorint

%o def A046028(n):

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

%o m, k = n, f(n)

%o while m != k:

%o m, k = k, f(k)

%o s = factorint(m)

%o return next(p for p in sorted(s,reverse=True) if s[p]>1) # _Chai Wah Wu_, Jul 22 2024

%Y Cf. A006530, A046027, A013929, A249740.

%Y Cf. A027748, A124010, A212177.

%K nonn,easy,nice

%O 1,1

%A _Eric W. Weisstein_