A366725 Sum of odd indices of distinct prime factors of n.

0, 1, 0, 1, 3, 1, 0, 1, 0, 4, 5, 1, 0, 1, 3, 1, 7, 1, 0, 4, 0, 6, 9, 1, 3, 1, 0, 1, 0, 4, 11, 1, 5, 8, 3, 1, 0, 1, 0, 4, 13, 1, 0, 6, 3, 10, 15, 1, 0, 4, 7, 1, 0, 1, 8, 1, 0, 1, 17, 4, 0, 12, 0, 1, 3, 6, 19, 8, 9, 4, 0, 1, 21, 1, 3, 1, 5, 1, 0, 4, 0, 14, 23, 1, 10, 1, 0, 6, 0, 4, 0, 10, 11, 16, 3, 1, 25, 1, 5, 4

Offset

1,5

Links

Table of n, a(n) for n=1..100.

Formula

G.f.: Sum_{k>=1} (2*k-1) * x^prime(2*k-1) / (1 - x^prime(2*k-1)).

Example

a(60) = 4 because 60 = 2^2 * 3 * 5 = prime(1)^2 * prime(2) * prime(3) and 1 + 3 = 4.

Mathematica

nmax = 100; CoefficientList[Series[Sum[(2 k - 1) x^Prime[2 k - 1]/(1 - x^Prime[2 k - 1]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A066207 (positions of 0's), A066328, A324966, A332422, A344908, A366528, A366784.

Sequence in context: A322512 A152892 A193002 * A122960 A242887 A307753

Adjacent sequences: A366722 A366723 A366724 * A366726 A366727 A366728

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 24 2023

Status

approved