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A373377 a(n) = gcd(A059975(n), A083345(n)), where A059975 is fully additive with a(p) = p-1, and A083345 is the numerator of the fully additive function with a(p) = 1/p.

%I A373377 #7 Jun 05 2024 19:23:09
%S A373377 0,1,1,1,1,1,1,3,2,1,1,4,1,1,2,2,1,1,1,6,2,1,1,1,2,1,1,8,1,1,1,5,2,1,
%T A373377 2,1,1,1,2,1,1,1,1,12,1,1,1,1,2,9,2,14,1,1,2,1,2,1,1,1,1,1,1,3,2,1,1,
%U A373377 18,2,1,1,1,1,1,1,20,2,1,1,1,4,1,1,1,2,1,2,1,1,1,2,24,2,1,2,1,1,1,1,1,1,1,1,1,1
%N A373377 a(n) = gcd(A059975(n), A083345(n)), where A059975 is fully additive with a(p) = p-1, and A083345 is the numerator of the fully additive function with a(p) = 1/p.
%C A373377 For each n >= 2, a(n) is a divisor of A373378(n).
%H A373377 Antti Karttunen, <a href="/A373377/b373377.txt">Table of n, a(n) for n = 1..65537</a>
%o A373377 (PARI)
%o A373377 A059975(n) = { my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*(f[i, 1] - 1)); };
%o A373377 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A373377 A373377(n) = gcd(A059975(n), A083345(n));
%Y A373377 Cf. A059975, A083345.
%Y A373377 Cf. A369002 (positions of even terms), A369003 (of odd terms).
%Y A373377 Cf. also A373363, A373368, A373369, A373378.
%K A373377 nonn
%O A373377 1,8
%A A373377 _Antti Karttunen_, Jun 05 2024