cp's OEIS Frontend

A082299 Greatest common divisor of n and its sum of prime factors (with repetition).

%I A082299 #15 Feb 01 2021 19:40:22
%S A082299 1,2,3,4,5,1,7,2,3,1,11,1,13,1,1,8,17,2,19,1,1,1,23,3,5,1,9,1,29,10,
%T A082299 31,2,1,1,1,2,37,1,1,1,41,6,43,1,1,1,47,1,7,2,1,1,53,1,1,1,1,1,59,12,
%U A082299 61,1,1,4,1,2,67,1,1,14,71,12,73,1,1,1,1,6,79,1,3,1,83,14,1,1,1,1,89,1,1,1,1
%N A082299 Greatest common divisor of n and its sum of prime factors (with repetition).
%C A082299 For n > 4, a(n) = n iff n is prime.
%H A082299 Antti Karttunen, <a href="/A082299/b082299.txt">Table of n, a(n) for n = 1..20000</a> (first 1000 terms from Harvey P. Dale)
%F A082299 a(n) = gcd(n, A001414(n)).
%F A082299 a(n) = n / A082344(n) = A001414(n) / A082343(n). - _Antti Karttunen_, Feb 01 2021
%e A082299 a(100) = GCD(2*2*5*5,2+2+5+5) = GCD(2*2*5,2*7) = 2;
%e A082299 a(200) = GCD(2*2*2*5*5,2+2+2+5+5) = GCD(2*2*2*5,2*2*2*2) = 8.
%t A082299 Table[GCD[Total[Times@@@FactorInteger[n]],n],{n,100}] (* _Harvey P. Dale_, Dec 27 2015 *)
%o A082299 (PARI)
%o A082299 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A082299 A082299(n) = gcd(n, A001414(n)); \\ _Antti Karttunen_, Feb 01 2021
%Y A082299 Cf. A001414, A082300 (positions of ones), A082343, A082344.
%Y A082299 Cf. also A099635, A099636.
%K A082299 nonn
%O A082299 1,2
%A A082299 _Reinhard Zumkeller_, Apr 08 2003