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A125604 Minimum of the largest prime factors of a number and its two neighbors.

%I A125604 #23 Jun 19 2025 00:10:50
%S A125604 2,2,2,3,2,2,2,3,3,3,3,5,2,2,2,3,3,5,5,7,3,3,3,3,3,3,5,5,2,2,2,7,3,3,
%T A125604 3,13,5,5,5,7,7,5,5,5,3,3,3,5,5,13,3,3,3,7,7,19,5,5,5,7,2,2,2,11,11,
%U A125604 17,7,7,3,3,3,5,5,5,11,11,5,3,3,3,7,7,7,17,11,11,5,5,5,13,23,19,3,3,3,7,5,5
%N A125604 Minimum of the largest prime factors of a number and its two neighbors.
%H A125604 Robert Israel, <a href="/A125604/b125604.txt">Table of n, a(n) for n = 3..10000</a>
%F A125604 a(n) = min{lpf(n-1),lpf(n),lpf(n+1)}, where lpf is the largest prime factor: lpf(k) = A006530(k).
%e A125604 a(93) = min{lpf(92),lpf(93),lpf(94)} = min{23,31,47} = 23.
%p A125604 LPF:= map(t -> max(numtheory:-factorset(t)), [$2..101]):
%p A125604 [seq](min(LPF[i..i+2]),i=1..nops(LPF)-2); # _Robert Israel_, Jun 16 2025
%t A125604 LPF = FactorInteger[ # ][[ -1, 1]] &; Map[Min[{LPF[ # - 1], LPF[ # ], LPF[ # + 1]}] &, Range[3, 200]]
%t A125604 Min/@Partition[Table[FactorInteger[n][[-1,1]],{n,110}],3,1] (* _Harvey P. Dale_, May 25 2015 *)
%o A125604 (PARI) a(n) = my(lpf(k)=vecmax(factor(k)[, 1])); vecmin([lpf(n-1), lpf(n), lpf(n+1)]); \\ _Ruud H.G. van Tol_, Aug 15 2024
%o A125604 (Python)
%o A125604 from sympy import primefactors
%o A125604 def a(n): return min(map(lambda n: primefactors(n)[-1], range(n-1,n+2))) # _David Radcliffe_, Jun 16 2025
%Y A125604 Cf. A006530, A093074.
%K A125604 nonn,look
%O A125604 3,1
%A A125604 _Carlos Alves_, Nov 27 2006