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A348045 Möbius transform of A252463, where A252463 shifts the prime factorization of odd numbers one step towards smaller primes and divides even numbers by two.

%I A348045 #14 Oct 14 2021 19:16:33
%S A348045 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 A348045 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 A348045 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 A348045 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 A348045 Antti Karttunen, <a href="/A348045/b348045.txt">Table of n, a(n) for n = 1..16384</a>
%H A348045 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A348045 a(n) = Sum_{d|n} A008683(n/d) * A252463(d).
%o A348045 (PARI)
%o A348045 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 A348045 A252463(n) = if(!(n%2),n/2,A064989(n));
%o A348045 A348045(n) = sumdiv(n,d,moebius(n/d)*A252463(d));
%Y A348045 Cf. A008683, A064989, A252463, A285702 (odd bisection), A348046 (positions of 2's).
%Y A348045 Cf. also A023022, A326305, A347115.
%K A348045 nonn,look
%O A348045 1,5
%A A348045 _Antti Karttunen_, Oct 12 2021