A086436 Maximum number of parts possible in a factorization of n; a(1) = 1, and for n > 1, a(n) = A001222(n) = bigomega(n).

1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 5, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 3, 6, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 5, 4, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 3, 2, 2, 2, 6, 1, 3, 3, 4, 1, 3

Offset: 1

Author

Eric W. Weisstein, Jul 19 2003

Keywords

• nonn

Comments

Incorrect (a(1)=0, not 1 as given here) duplicate of A001222. - Joerg Arndt, Jul 22 2017

Examples

			a(6)=2 since 6 may be factored as {{2,3},{6}}, so the largest number of factors possible is 2 {2,3}.
a(8)=3 since 8 may be factored as {{8},{2,2,2},{2,4}}, so the largest numbers of factors possible is 3 {2,2,2}.
a(30)=3 since 30 may be factored as {{30},{2,3,5},{5,6},{3,10},{2,15}}, so the largest numbers of factors possible is 3 {2,3,5}.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024
• Eric Weisstein's World of Mathematics, Unordered Factorization

Crossrefs

Essentially the same as A001222.

Programs

Mathematica

Join[{1},PrimeOmega[Range[2,110]]] (* Harvey P. Dale, Jun 20 2013 *)

MuPAD

numlib::Omega (n)$ n=1..102 // Zerinvary Lajos, May 13 2008

Extensions

Alternative description added to the name by Antti Karttunen, Oct 21 2017