A077327 - OEIS

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..17.

EXAMPLE

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

PROG

(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

CROSSREFS

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

Cf. A106411-A106419, A106421-A106429.

Sequence in context: A109107 A037729 A037624 * A173499 A067636 A226301

Adjacent sequences: A077324 A077325 A077326 * A077328 A077329 A077330

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Nov 04 2002

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

STATUS

approved