A363895 Floor of the average of the distinct prime factors of n.

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

Offset: 2

Author

Darío Clavijo, Jun 26 2023

Keywords

• easy
• nonn

Crossrefs

Cf. A126594, A008472, A001221, A078174, A323171, A323172.

Programs

Mathematica

a[n_] := Floor[Mean[FactorInteger[n][[;; , 1]]]]; Array[a, 100, 2] (* Amiram Eldar, Jun 27 2023 *)

PARI

a(n) = my(p = factor(n)[, 1]); vecsum(p)\#p; \\ Amiram Eldar, Jun 29 2023

Python

from sympy import factorint
def a(n):
  P = factorint(n).keys()
  return int(sum(P)/len(P))
print([a(n) for n in range(2, 85)])

Formula

a(p^n) = p, p prime, n >= 1.

a(n) = floor(A008472(n)/A001221(n)).

a(n) = floor(A323171(n)/A323172(n)).