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

2,1

Links

Table of n, a(n) for n=2..79.

Formula

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

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A273288 A080210 A126594 * A086765 A079868 A280697

Adjacent sequences: A363892 A363893 A363894 * A363896 A363897 A363898

Keyword

easy,nonn

Author

Darío Clavijo, Jun 26 2023

Status

approved