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Smallest multiple prime factor of the n-th nonsquarefree number (A013929).
6

%I #24 Jul 23 2024 10:53:40

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

%H Amiram Eldar, <a href="/A046027/b046027.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%F a(n) = A249739(A013929(n)). - _Amiram Eldar_, Feb 11 2021

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

%o (Python)

%o from math import isqrt

%o from sympy import mobius, factorint

%o def A046027(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) if s[p]>1) # _Chai Wah Wu_, Jul 22 2024

%Y Cf. A013929, A020639, A046028, A249739.

%K nonn

%O 1,1

%A _Eric W. Weisstein_