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%I #14 Oct 14 2021 19:16:33
%S 1,0,1,1,2,1,4,2,2,2,6,2,10,2,2,4,12,4,16,4,4,4,18,4,6,2,4,6,22,6,28,
%T 8,6,4,8,6,30,2,10,8,36,8,40,10,4,4,42,8,20,14,12,12,46,14,12,12,16,6,
%U 52,8,58,2,8,16,20,14,60,16,18,16,66,12,70,6,6,18,24,14,72,16,8,4,78,12,24,2,22,20,82,20
%N Möbius transform of A252463, where A252463 shifts the prime factorization of odd numbers one step towards smaller primes and divides even numbers by two.
%H Antti Karttunen, <a href="/A348045/b348045.txt">Table of n, a(n) for n = 1..16384</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} A008683(n/d) * A252463(d).
%o (PARI)
%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A252463(n) = if(!(n%2),n/2,A064989(n));
%o A348045(n) = sumdiv(n,d,moebius(n/d)*A252463(d));
%Y Cf. A008683, A064989, A252463, A285702 (odd bisection), A348046 (positions of 2's).
%Y Cf. also A023022, A326305, A347115.
%K nonn,look
%O 1,5
%A _Antti Karttunen_, Oct 12 2021
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