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Inverse Möbius transform of A353370.
3

%I #10 Apr 20 2022 09:58:34

%S 1,1,1,1,1,2,1,1,1,1,1,2,1,2,2,1,1,2,1,1,1,1,1,2,1,2,1,2,1,3,1,1,2,1,

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

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

%N Inverse Möbius transform of A353370.

%C Number of terms of A325698 that divide n.

%H Antti Karttunen, <a href="/A353372/b353372.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = Sum_{d|n} A353370(d).

%F a(n) = A000005(n) - A353371(n).

%F a(p) = 1 for all primes p.

%F a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.

%o (PARI)

%o A353370(n) = { my(f = factor(n)); (0==sum(i=1, #f~, f[i,2]*((-1)^(primepi(f[i, 1])%2)))); };

%o A353372(n) = sumdiv(n,d,A353370(d));

%Y Cf. A000005, A003961, A325698, A353370, A353371.

%K nonn

%O 1,6

%A _Antti Karttunen_, Apr 16 2022