A353417 - OEIS

%I #9 Apr 20 2022 22:48:30

%S 1,1,1,1,3,3,4,1,1,4,5,3,7,5,3,1,8,8,10,4,4,7,11,3,8,8,1,5,13,14,16,1,

%T 5,10,14,8,17,11,7,4,20,18,22,7,3,13,23,3,17,17,8,8,25,22,18,5,10,16,

%U 28,14,31,17,4,1,26,26,32,10,11,26,35,8,37,20,8,11,26,30,38,4,1,22,41,18,30,23,13,7,43,42

%N a(n) = A113415(A252463(n)), where A113415 is the arithmetic mean between the number of odd divisors and their sum, and A252463 is the hybrid shift.

%C Arithmetic mean between A320107(n) and A353416(n).

%H Antti Karttunen, <a href="/A353417/b353417.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>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A113415(A252463(n)) = A113415(A353412(n)).

%F a(n) = (1/2) * (A320107(n) + A353416(n)).

%F a(2*n) = A113415(n).

%o (PARI)

%o A000265(n) = (n>>valuation(n,2));

%o A064989(n) = { my(f=factor(A000265(n))); 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 A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));

%o A353417(n) = A113415(A252463(n));

%Y Cf. A000203, A064989, A113415 (even bisection), A252463, A320107, A353412, A353416.

%K nonn

%O 1,5

%A _Antti Karttunen_, Apr 20 2022