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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). 9
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Incorrect (a(1)=0, not 1 as given here) duplicate of A001222. - Joerg Arndt, Jul 22 2017 LINKS Antti Karttunen, Table of n, a(n) for n = 1..1024 Eric Weisstein's World of Mathematics, Unordered Factorization EXAMPLE 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}. MATHEMATICA Join[{1}, PrimeOmega[Range[2, 110]]] (* Harvey P. Dale, Jun 20 2013 *) PROG (MuPAD) numlib::Omega (n)\$ n=1..102 // Zerinvary Lajos, May 13 2008 CROSSREFS Essentially the same as A001222. Sequence in context: A277013 A305822 A326190 * A001222 A257091 A319269 Adjacent sequences:  A086433 A086434 A086435 * A086437 A086438 A086439 KEYWORD nonn AUTHOR Eric W. Weisstein, Jul 19 2003 EXTENSIONS Alternative description added to the name by Antti Karttunen, Oct 21 2017 STATUS approved

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Last modified September 19 08:05 EDT 2021. Contains 347556 sequences. (Running on oeis4.)