A123528 Numerator of average of prime factors of n.

2, 3, 2, 5, 5, 7, 2, 3, 7, 11, 7, 13, 9, 4, 2, 17, 8, 19, 3, 5, 13, 23, 9, 5, 15, 3, 11, 29, 10, 31, 2, 7, 19, 6, 5, 37, 21, 8, 11, 41, 4, 43, 5, 11, 25, 47, 11, 7, 4, 10, 17, 53, 11, 8, 13, 11, 31, 59, 3, 61, 33, 13, 2, 9, 16, 67, 7, 13, 14, 71, 12, 73, 39, 13, 23, 9, 6, 79, 13, 3, 43, 83, 7

Offset

2,1

Links

G. C. Greubel, Table of n, a(n) for n = 2..5000

Formula

a(n) = sopfr(n) / bigomega(n) = A001414(n) / A001222(n).

Example

12 = 2 * 2 * 3, so a(12) = (2 + 2 + 3) / 3 = 7/3.
Sequence of fractions starts 2/1, 3/1, 2/1, 5/1, 5/2, 7/1, 2/1, 3/1, 7/2, 11/1, 7/3.

Mathematica

f[n_] := Plus @@ Times @@@ FactorInteger@n; f[1] = 0; Numerator[ Table[ f[n]/PrimeOmega[n], {n, 2, 50}]] (* G. C. Greubel, Oct 14 2017 *)

Crossrefs

Cf. A123529, A067629, A001414, A001222.

Sequence in context: A323171 A008472 A318675 * A374250 A074036 A074251

Adjacent sequences: A123525 A123526 A123527 * A123529 A123530 A123531

Keyword

frac,nonn

Author

Franklin T. Adams-Watters, Oct 02 2006

Status

approved