A077327 Smallest number beginning with 2 and having exactly n distinct prime divisors.

2, 20, 204, 210, 2310, 200970, 2012010, 20030010, 223092870, 20090100030, 200560490130, 20055767721990, 2000029432190790, 20384767656323070, 2000848249650860610, 200001648981983238390, 2183473617971732996910

Offset: 1

Author

Amarnath Murthy, Nov 04 2002

Keywords

• base
• nonn

Examples

			a(1) = 2, a(5) = 2310 = 2*3*5*7*11.
		

Crossrefs

Cf. A077326, A077328, A077329, A077330, A077331, A077332, A077333, A077334.

Cf. A106411-A106419, A106421-A106429.

Programs

Python

from sympy import primorial, factorint
def a(n, begins_with=2): # use begins_with 1-9 for A077326-A077334
  m, start_digit = primorial(n), str(begins_with)
  while len(factorint(m)) != n or str(m)[0] != start_digit:
    m += 1
    s = str(m)
    if s[0] == start_digit: continue
    elif s[0] < start_digit: m = int(start_digit+'0'*(len(s)-1))
    else: m = int(start_digit+'0'*len(s))
  return m
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Feb 20 2021

Extensions

Correct a(2) and a(3), add a(6)-a(11) from Ray Chandler, Apr 17 2005

More terms from Ray Chandler, May 02 2005