A036337 - OEIS

%I #32 Sep 02 2022 13:17:42

%S 7,95,994,9999,99996,999992,9999968,99999840,999999968,9999999900,

%T 99999999840,999999999744,9999999998720,99999999998400,

%U 999999999999000,9999999999999744,99999999999995904,999999999999967232,9999999999999989760,99999999999999995904

%N Largest integer with n digits and exactly n prime factors (counted with multiplicity).

%C If all prime factors are distinct then a(n) >= A002110(n) which might give a contradiction for large enough n and so some primes have a multiplicity > k for some nonnegative k. - _David A. Corneth_, Oct 30 2018

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_025.htm">Puzzle 25. Composed primes (by G.L. Honaker, Jr.)</a>, The Prime Puzzles and Problems Connection. (A related puzzle.)

%e 95 = 5 * 19, while 96, 97, 98, 99 and 100 have, respectively, 6,1,3,3 and 4 prime factors; thus 95 is the largest two digit number with exactly two prime factors.

%t Table[Module[{k=10^n-1},While[PrimeOmega[k]!=n,k--];k],{n,20}] (* _Harvey P. Dale_, Sep 02 2022 *)

%o (PARI) a(n) = forstep(i = 10^n-1,10^(n-1),-1,if(bigomega(i) == n, return(i))) \\ _David A. Corneth_, Oct 30 2018

%Y Cf. A002110, A036335, A036336, A036338.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Dec 15 1998

%E More terms and better description from _Matthew Conroy_, May 25 2001

%E a(19) and a(20) from _Zak Seidov_, Oct 30 2018