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

1,1

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.

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 *)

Prog

(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

Crossrefs

Cf. A036335, A036337, A036338.

Sequence in context: A228120 A074109 A291101 * A070842 A086927 A342108

Adjacent sequences: A036333 A036334 A036335 * A036337 A036338 A036339

Keyword

nonn,base

Author

Patrick De Geest, Dec 15 1998

Extensions

More terms from Matthew Conroy, May 27 2001

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

Status

approved