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A353382 Inverse Möbius transform of A353380.

%I A353382 #10 Apr 19 2022 22:45:38
%S A353382 1,1,1,2,1,2,1,3,2,1,1,4,1,2,2,3,1,4,1,3,1,1,1,5,2,2,3,4,1,3,1,4,2,1,
%T A353382 2,7,1,2,1,4,1,3,1,3,4,1,1,6,2,3,2,4,1,5,1,5,1,2,1,7,1,1,3,5,2,3,1,3,
%U A353382 2,3,1,9,1,2,4,4,2,3,1,4,3,1,1,7,1,2,1,4,1,7,1,3,2,1,2,8,1,4,4,6,1,3,1,5,3
%N A353382 Inverse Möbius transform of A353380.
%C A353382 Number of terms of A353355 that divide n.
%H A353382 Antti Karttunen, <a href="/A353382/b353382.txt">Table of n, a(n) for n = 1..65537</a>
%H A353382 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353382 a(n) = Sum_{d|n} A353380(d).
%F A353382 a(n) = A000005(n) - A353381(n).
%F A353382 a(p) = 1 for all primes p.
%F A353382 a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
%o A353382 (PARI)
%o A353382 A332823(n) = { my(f = factor(n),u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u,-1,u); };
%o A353382 A353354(n) = sumdiv(n,d,A332823(d));
%o A353382 A353380(n) = (0==A353354(n));
%o A353382 A353382(n) = sumdiv(n,d,A353380(d));
%Y A353382 Cf. A000005, A003961, A048675, A332823, A348717, A353352, A353354, A353355, A353380, A353381.
%K A353382 nonn
%O A353382 1,4
%A A353382 _Antti Karttunen_, Apr 19 2022