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A373364 a(n) = gcd(A001414(n), A003415(n)), where A001414 is the sum of prime factors with repetition, and A003415 is the arithmetic derivative.

%I A373364 #10 Jun 04 2024 07:39:33
%S A373364 0,1,1,4,1,5,1,6,6,7,1,1,1,9,8,8,1,1,1,3,10,13,1,1,10,15,9,1,1,1,1,10,
%T A373364 14,19,12,10,1,21,16,1,1,1,1,3,1,25,1,1,14,3,20,1,1,1,16,1,22,31,1,4,
%U A373364 1,33,1,12,18,1,1,3,26,1,1,12,1,39,1,1,18,1,1,1,12,43,1,2,22,45,32,1,1,1,20,3,34,49,24
%N A373364 a(n) = gcd(A001414(n), A003415(n)), where A001414 is the sum of prime factors with repetition, and A003415 is the arithmetic derivative.
%C A373364 For n >= 1, a(n) is a multiple of A373363(n).
%H A373364 Antti Karttunen, <a href="/A373364/b373364.txt">Table of n, a(n) for n = 1..65537</a>
%o A373364 (PARI)
%o A373364 A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
%o A373364 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A373364 A373364(n) = gcd(A001414(n), A003415(n));
%Y A373364 Cf. A001414, A003415, A373375 (positions of even terms), A373376 (of odd terms).
%Y A373364 Cf. also A082299, A373362, A373363.
%K A373364 nonn
%O A373364 1,4
%A A373364 _Antti Karttunen_, Jun 02 2024