A378444 - OEIS

%I #7 Nov 27 2024 17:56:14

%S 1,1,1,1,1,1,1,1,2,1,1,2,1,1,2,2,1,2,1,2,2,1,1,2,2,1,2,2,1,2,1,2,2,1,

%T 2,3,1,1,2,2,1,2,1,2,3,1,1,3,2,2,2,2,1,2,2,2,2,1,1,4,1,1,3,2,2,2,1,2,

%U 2,2,1,3,1,1,3,2,2,2,1,3,3,1,1,4,2,1,2,2,1,3,2,2,2,1,2,3,1,2,3,3,1,2,1,2,4

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

%C Number of terms of A369002 that divide n.

%H Antti Karttunen, <a href="/A378444/b378444.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = Sum_{d|n} A369001(d).

%F a(n) = A000005(n) - A378445(n).

%o (PARI)

%o A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };

%o A369001(n) = !(A083345(n)%2);

%o A378444(n) = sumdiv(n,d,A369001(d));

%Y Inverse Möbius transform of A369001.

%Y Cf. A000005, A369002, A378445.

%Y Cf. also A369257.

%K nonn

%O 1,9

%A _Antti Karttunen_, Nov 27 2024