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A099636 a(n) = gcd(sum of distinct prime factors of n, product of distinct prime factors of n).

%I A099636 #20 Feb 01 2021 19:40:42
%S A099636 1,2,3,2,5,1,7,2,3,1,11,1,13,1,1,2,17,1,19,1,1,1,23,1,5,1,3,1,29,10,
%T A099636 31,2,1,1,1,1,37,1,1,1,41,6,43,1,1,1,47,1,7,1,1,1,53,1,1,1,1,1,59,10,
%U A099636 61,1,1,2,1,2,67,1,1,14,71,1,73,1,1,1,1,6,79,1,3,1,83,6,1,1,1,1,89,10,1,1,1
%N A099636 a(n) = gcd(sum of distinct prime factors of n, product of distinct prime factors of n).
%H A099636 Antti Karttunen, <a href="/A099636/b099636.txt">Table of n, a(n) for n = 1..20000</a>
%F A099636 From _Antti Karttunen_, Feb 01 2021: (Start)
%F A099636 a(n) = gcd(A007947(n), A008472(n)).
%F A099636 a(n) = A007947(n) / A340677(n) = A008472(n) / A340678(n).
%F A099636 (End)
%e A099636 n=84: a(84) = gcd(2*3*7, 2+3+7) = gcd(42, 12) = 6.
%t A099636 PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; f[n_] := Block[{pf = PrimeFactors[n]}, GCD[Plus @@ pf, Times @@ pf]]; Table[ f[n], {n, 93}] (* _Robert G. Wilson v_, Nov 04 2004 *)
%o A099636 (PARI)
%o A099636 A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947
%o A099636 A008472(n) = vecsum(factor(n)[, 1]); \\ From A008472
%o A099636 A099636(n) = gcd(A007947(n), A008472(n));
%Y A099636 Cf. A007947, A008472, A082299, A099634, A340677, A340678.
%Y A099636 Differs from related A099635 for the first time at n=84, where a(84) = 6, while A099635(84) = 12.
%Y A099636 Differs from A014963 for the first time at n=30, where a(30) = 10, while A014963(30) = 1.
%K A099636 nonn
%O A099636 1,2
%A A099636 _Labos Elemer_, Oct 28 2004
%E A099636 Name clarified by _Antti Karttunen_, Feb 01 2021