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A353416 a(n) = A000593(A252463(n)), where A000593 is the sum of odd divisors, and A252463 is the hybrid shift.

%I A353416 #11 Apr 20 2022 22:48:26
%S A353416 1,1,1,1,4,4,6,1,1,6,8,4,12,8,4,1,14,13,18,6,6,12,20,4,13,14,1,8,24,
%T A353416 24,30,1,8,18,24,13,32,20,12,6,38,32,42,12,4,24,44,4,31,31,14,14,48,
%U A353416 40,32,8,18,30,54,24,60,32,6,1,48,48,62,18,20,48,68,13,72,38,13,20,48,56,74,6,1,42,80,32,56,44,24
%N A353416 a(n) = A000593(A252463(n)), where A000593 is the sum of odd divisors, and A252463 is the hybrid shift.
%H A353416 Antti Karttunen, <a href="/A353416/b353416.txt">Table of n, a(n) for n = 1..16384</a>
%H A353416 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A353416 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A353416 a(n) = A000593(A252463(n)) = A000203(A353412(n)).
%F A353416 a(2*n) = A000593(n).
%F A353416 a(n) <= A000593(n) for all n >= 1.
%o A353416 (PARI)
%o A353416 A000265(n) = (n>>valuation(n,2));
%o A353416 A000593(n) = sigma(A000265(n));
%o A353416 A064989(n) = { my(f=factor(A000265(n))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
%o A353416 A252463(n) = if(!(n%2),n/2,A064989(n));
%o A353416 A353416(n) = A000593(A252463(n));
%Y A353416 Cf. A000203, A000265, A000593 (even bisection), A064989, A252463, A353412.
%Y A353416 Cf. also A320107, A353417.
%K A353416 nonn
%O A353416 1,5
%A A353416 _Antti Karttunen_, Apr 20 2022