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

%I A086436 #46 Feb 16 2025 08:32:50
%S A086436 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,
%T A086436 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,
%U A086436 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
%N A086436 Maximum number of parts possible in a factorization of n; a(1) = 1, and for n > 1, a(n) = A001222(n) = bigomega(n).
%C A086436 Incorrect (a(1)=0, not 1 as given here) duplicate of A001222. - _Joerg Arndt_, Jul 22 2017
%H A086436 Antti Karttunen, <a href="/A086436/b086436.txt">Table of n, a(n) for n = 1..1024</a>
%H A086436 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnorderedFactorization.html">Unordered Factorization</a>
%e A086436 a(6)=2 since 6 may be factored as {{2,3},{6}}, so the largest number of factors possible is 2 {2,3}.
%e A086436 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}.
%e A086436 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}.
%t A086436 Join[{1},PrimeOmega[Range[2,110]]] (* _Harvey P. Dale_, Jun 20 2013 *)
%o A086436 (MuPAD) numlib::Omega (n)$ n=1..102 // _Zerinvary Lajos_, May 13 2008
%Y A086436 Essentially the same as A001222.
%K A086436 nonn
%O A086436 1,4
%A A086436 _Eric W. Weisstein_, Jul 19 2003
%E A086436 Alternative description added to the name by _Antti Karttunen_, Oct 21 2017