A036337 Largest integer with n digits and exactly n prime factors (counted with multiplicity).

7, 95, 994, 9999, 99996, 999992, 9999968, 99999840, 999999968, 9999999900, 99999999840, 999999999744, 9999999998720, 99999999998400, 999999999999000, 9999999999999744, 99999999999995904, 999999999999967232, 9999999999999989760, 99999999999999995904

Offset: 1

Author

Patrick De Geest, Dec 15 1998

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

• Carlos Rivera, Puzzle 25. Composed primes (by G.L. Honaker, Jr.), The Prime Puzzles and Problems Connection. (A related puzzle.)

Crossrefs

Cf. A002110, A036335, A036336, A036338.

Programs

Mathematica

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

PARI

a(n) = forstep(i = 10^n-1,10^(n-1),-1,if(bigomega(i) == n, return(i))) \\ David A. Corneth, Oct 30 2018

Extensions

More terms and better description from Matthew Conroy, May 25 2001

a(19) and a(20) from Zak Seidov, Oct 30 2018