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

Author

Lekraj Beedassy, Aug 30 2006

Keywords

• nonn

Comments

a(n) = 1 iff n is prime.

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

Formula

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

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

Extensions

Edited and extended by Ray Chandler, Sep 11 2006