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

1,5

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)

Formula

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

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

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

Prog

(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));

Crossrefs

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

Sequence in context: A243823 A281141 A078911 * A082899 A249491 A309888

Adjacent sequences: A353414 A353415 A353416 * A353418 A353419 A353420

Keyword

nonn

Author

Antti Karttunen, Apr 20 2022

Status

approved