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A353412 The odd part of hybrid shift: a(n) = A000265(A252463(n)).

%I A353412 #18 Apr 18 2022 22:33:42
%S A353412 1,1,1,1,3,3,5,1,1,5,7,3,11,7,3,1,13,9,17,5,5,11,19,3,9,13,1,7,23,15,
%T A353412 29,1,7,17,15,9,31,19,11,5,37,21,41,11,3,23,43,3,25,25,13,13,47,27,21,
%U A353412 7,17,29,53,15,59,31,5,1,33,33,61,17,19,35,67,9,71,37,9,19,35,39,73,5,1,41,79,21,39,43,23,11
%N A353412 The odd part of hybrid shift: a(n) = A000265(A252463(n)).
%H A353412 Antti Karttunen, <a href="/A353412/b353412.txt">Table of n, a(n) for n = 1..16384</a>
%H A353412 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353412 a(n) = A000265(A252463(n)).
%F A353412 a(2*n) = A000265(n), a(2*n-1) = A353413(n) = A000265(A064216(n)).
%F A353412 For all n >= 1, A000005(a(n)) = A320107(n).
%o A353412 (PARI)
%o A353412 A000265(n) = (n>>valuation(n,2));
%o A353412 A064989(n) = { my(f=factor(A000265(n))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A353412 A252463(n) = if(!(n%2),n/2,A064989(n));
%o A353412 A353412(n) = A000265(A252463(n));
%o A353412 (Python)
%o A353412 from math import prod
%o A353412 from sympy import factorint, prevprime
%o A353412 def A353412(n): return int(bin(prod(1 if p == 2 else prevprime(p)*e for p, e in factorint(n).items()) if n % 2 else n//2)[2:].rstrip('0'),2) # _Chai Wah Wu_, Apr 18 2022
%Y A353412 Cf. A000005, A252463, A064216, A064989, A320107.
%Y A353412 Cf. A000265 (even bisection), A353413 (odd bisection).
%K A353412 nonn
%O A353412 1,5
%A A353412 _Antti Karttunen_, Apr 18 2022