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a(n) is the number of divisors d of n such that A083345(d) is odd, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).
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%I #7 Nov 27 2024 17:56:18

%S 0,1,1,2,1,3,1,3,1,3,1,4,1,3,2,3,1,4,1,4,2,3,1,6,1,3,2,4,1,6,1,4,2,3,

%T 2,6,1,3,2,6,1,6,1,4,3,3,1,7,1,4,2,4,1,6,2,6,2,3,1,8,1,3,3,5,2,6,1,4,

%U 2,6,1,9,1,3,3,4,2,6,1,7,2,3,1,8,2,3,2,6,1,9,2,4,2,3,2,9,1,4,3,6,1,6,1,6,4

%N a(n) is the number of divisors d of n such that A083345(d) is odd, where A083345(n) is the numerator of Sum(e/p: n=Product(p^e)).

%C Number of terms of A369003 that divide n.

%H Antti Karttunen, <a href="/A378445/b378445.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = Sum_{d|n} A377874(d).

%F a(n) = A000005(n) - A378444(n).

%o (PARI)

%o A377874(n) = { my(f=factor(n)); (numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1])))%2); };

%o A378445(n) = sumdiv(n,d,A377874(d));

%Y Inverse Möbius transform of A377874.

%Y Cf. A000005, A369003, A378444.

%Y Cf. also A174273, A378443.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 27 2024