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Largest prime less than greatest prime factor of n but not dividing n, or 1 if no such prime exists.
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%I #13 Feb 21 2021 03:40:27

%S 1,1,2,1,3,1,5,1,2,3,7,1,11,5,2,1,13,1,17,3,5,7,19,1,3,11,2,5,23,1,29,

%T 1,7,13,3,1,31,17,11,3,37,5,41,7,2,19,43,1,5,3,13,11,47,1,7,5,17,23,

%U 53,1,59,29,5,1,11,7,61,13,19,3,67,1,71,31,2,17,5,11,73,3,2,37,79,5,13,41,23

%N Largest prime less than greatest prime factor of n but not dividing n, or 1 if no such prime exists.

%H Alois P. Heinz, <a href="/A079068/b079068.txt">Table of n, a(n) for n = 1..20000</a>

%p a:= proc(n) local p, s; s:= numtheory[factorset](n);

%p if s={} then return 1

%p else p:= max(s);

%p do if p=2 then return 1 else p:= prevprime(p) fi;

%p if not p in s then return p fi

%p od

%p fi

%p end:

%p seq(a(n), n=1..100); # _Alois P. Heinz_, Sep 03 2019

%t a[n_] := Module[{p}, For[p = NextPrime[FactorInteger[n][[-1, 1]], -1], p>1, p = NextPrime[p, -1], If[!Divisible[n, p], Return[p]]]; 1];

%t Array[a, 100] (* _Jean-François Alcover_, Nov 04 2020 *)

%Y Cf. A079067, A006530.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Dec 20 2002