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A373485 a(n) = gcd(A083345(n), A276085(n)), where A276085 is fully additive with a(p) = p#/p, and A083345 is the numerator of the fully additive function with a(p) = 1/p.

%I A373485 #10 Jun 09 2024 13:21:17
%S A373485 0,1,1,1,1,1,1,3,2,7,1,4,1,1,8,2,1,1,1,2,2,1,1,1,2,1,1,8,1,1,1,5,2,1,
%T A373485 12,1,1,1,8,1,1,1,1,4,1,1,1,1,2,1,4,2,1,1,8,1,2,1,1,1,1,1,17,3,6,1,1,
%U A373485 2,2,1,1,1,1,1,1,4,6,1,1,1,4,1,1,1,2,1,8,1,1,1,20,4,2,1,12,1,1,1,1,7,1,1,1,1,1
%N A373485 a(n) = gcd(A083345(n), A276085(n)), where A276085 is fully additive with a(p) = p#/p, and A083345 is the numerator of the fully additive function with a(p) = 1/p.
%C A373485 For all n >= 1, A373145(n) is a multiple of a(n).
%C A373485 For all i, j: A373151(i) = A373151(j) => a(i) = a(j) => A373483(i) = A373483(j).
%H A373485 Antti Karttunen, <a href="/A373485/b373485.txt">Table of n, a(n) for n = 1..100000</a>
%o A373485 (PARI)
%o A373485 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A373485 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
%o A373485 A373485(n) = gcd(A083345(n), A276085(n));
%Y A373485 Cf. A083345, A276085, A373145, A373151.
%Y A373485 Cf. A369002 (positions of even terms), A369003 (of odd terms), A373483, A373484 (of multiples of 3).
%K A373485 nonn
%O A373485 1,8
%A A373485 _Antti Karttunen_, Jun 09 2024