A366873 a(n) = A113415(A163511(n)), where A113415(n) is the average of number of and sum of odd divisors of n.

1, 1, 1, 3, 1, 8, 3, 4, 1, 22, 8, 17, 3, 14, 4, 5, 1, 63, 22, 80, 8, 65, 17, 30, 3, 42, 14, 26, 4, 18, 5, 7, 1, 185, 63, 393, 22, 316, 80, 202, 8, 206, 65, 174, 17, 117, 30, 68, 3, 124, 42, 127, 14, 100, 26, 50, 4, 55, 18, 38, 5, 26, 7, 8, 1, 550, 185, 1956, 63, 1567, 393, 1403, 22, 1020, 316, 1204, 80, 804, 202

Offset: 0

Author

Antti Karttunen, Oct 27 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A113415, A163511, A366874 (rgs-transform).

Cf. also A324186, A366797, A366875.

Programs

PARI

A113415(n) = if(n<1, 0, sumdiv(n, d, if(d%2, (d+1)/2)));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A366873(n) = A113415(A163511(n));

Formula

a(n) = (1/2) * (A324186(n)+A366797(n)).