A379141 If n = Product (p_j^k_j) then a(n) = numerator of Sum 1/k_j.

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 5, 1, 2, 3, 1, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 5, 1, 2, 1, 5, 2, 2, 2, 4, 1, 5, 2, 3, 2, 2, 2, 6, 1, 3, 3, 1, 1, 3, 1, 4, 3, 2, 1, 5, 1, 3

Offset

1,6

Links

Table of n, a(n) for n=1..110.

Maple

a:= n-> numer(add(1/i[2], i=ifactors(n)[2])):
seq(a(n), n=1..110);  # Alois P. Heinz, Dec 16 2024

Mathematica

Join[{0}, Table[Plus @@ (1/#[[2]] & /@ FactorInteger[n]), {n, 2, 110}]] // Numerator

Prog

(PARI) a(n) = my(f=factor(n)); numerator(sum(k=1, #f~, 1/f[k, 2])); \\ Michel Marcus, Dec 16 2024

Crossrefs

Cf. A001222, A005361, A028235, A028236.

Sequence in context: A324191 A373957 A238946 * A351414 A349056 A326516

Adjacent sequences: A379138 A379139 A379140 * A379142 A379143 A379144

Keyword

nonn,frac,new

Author

Ilya Gutkovskiy, Dec 16 2024

Status

approved