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

Author

Ilya Gutkovskiy, Dec 16 2024

Keywords

• nonn
• frac

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A005361, A028235, A028236.

Programs

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

PARI

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