A353417 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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Apr 20 2022

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

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

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A064989(n) = { my(f=factor(A000265(n))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A252463(n) = if(!(n%2),n/2,A064989(n));
A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
A353417(n) = A113415(A252463(n));

Formula

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

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

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