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

1,1

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

Links

Table of n, a(n) for n=1..20.

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A002110, A036335, A036336, A036338.

Sequence in context: A015225 A183521 A342109 * A186378 A244856 A367159

Adjacent sequences: A036334 A036335 A036336 * A036338 A036339 A036340

Keyword

nonn,base

Author

Patrick De Geest, Dec 15 1998

Extensions

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

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

Status

approved