A122375 Number of distinct prime factors of the smallest number with exactly n divisors.

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

Offset

1,4

Comments

a(n) = 1 iff n is prime.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 2000 terms from Antti Karttunen)

Formula

a(n) = omega(A005179(n)), where omega(n) = A001221(n).

a(n) = A001221(A130279(n)). - Reinhard Zumkeller, May 21 2007

Example

a(14) = 2 as A005179(14) = 192 which has 2 distinct prime divisors (2 and 3). - David A. Corneth, Dec 10 2021

Mathematica

A005179 = Cases[Import["https://oeis.org/A005179/b005179.txt", "Table"], {_, _}][[All, 2]];
a[n_] := PrimeNu[A005179[[n]]];
a /@ Range[2000] (* Jean-François Alcover, Mar 06 2020 *)

Crossrefs

Cf. A001221, A005179, A038457, A122810, A130279.

Sequence in context: A372502 A345222 A327399 * A038548 A320732 A305149

Adjacent sequences: A122372 A122373 A122374 * A122376 A122377 A122378

Keyword

nonn

Author

Lekraj Beedassy, Aug 30 2006

Extensions

Edited and extended by Ray Chandler, Sep 11 2006

Status

approved