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A082299 Greatest common divisor of n and its sum of prime factors (with repetition). 9

%I #15 Feb 01 2021 19:40:22

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

%C For n > 4, a(n) = n iff n is prime.

%H 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 a(n) = gcd(n, A001414(n)).

%F a(n) = n / A082344(n) = A001414(n) / A082343(n). - _Antti Karttunen_, Feb 01 2021

%e a(100) = GCD(2*2*5*5,2+2+5+5) = GCD(2*2*5,2*7) = 2;

%e a(200) = GCD(2*2*2*5*5,2+2+2+5+5) = GCD(2*2*2*5,2*2*2*2) = 8.

%t Table[GCD[Total[Times@@@FactorInteger[n]],n],{n,100}] (* _Harvey P. Dale_, Dec 27 2015 *)

%o (PARI)

%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.

%o A082299(n) = gcd(n, A001414(n)); \\ _Antti Karttunen_, Feb 01 2021

%Y Cf. A001414, A082300 (positions of ones), A082343, A082344.

%Y Cf. also A099635, A099636.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Apr 08 2003

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