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A366725
Sum of odd indices of distinct prime factors of n.
1
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 24 2023
STATUS
approved