A036336 Smallest positive integer with n digits and exactly n prime factors (counted with multiplicity).

2, 10, 102, 1012, 10010, 100040, 1000125, 10000096, 100000032, 1000000080, 10000000080, 100000000512, 1000000001280, 10000000014336, 100000000004096, 1000000000010880, 10000000000008192, 100000000000008192, 1000000000000010240, 10000000000000045056

Offset: 1

Author

Patrick De Geest, Dec 15 1998

Keywords

• nonn
• base

Links

• David A. Corneth, Table of n, a(n) for n = 1..29
• Carlos Rivera, Puzzle 25. Composed primes, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A036335, A036337, A036338.

Programs

Maple

f:= proc(n) local k;
  for k from 10^(n-1) do
    if numtheory:-bigomega(k) = n then return k fi
  od
end proc:
map(f, [$1..20]); # Robert Israel, May 31 2018

Mathematica

npf[n_]:=Module[{k=1,st=10^(n-1)-1},While[PrimeOmega[st+k]!=n,k++];st+k]; Array[npf,20] (* Harvey P. Dale, Mar 25 2012 *)

Python

from sympy import factorint
def a(n):
  for m in range(10**(n-1), 10**n):
    if sum(factorint(m).values()) == n: return m
print([a(n) for n in range(1, 13)]) # Michael S. Branicky, Feb 10 2021

Extensions

More terms from Matthew Conroy, May 27 2001

Offset corrected, and a(19)-a(20) from Robert Israel, May 31 2018