A192010 The smallest number with n digits in its prime factorization (total count of digits of all bases and exponents).

1, 4, 12, 36, 132, 396, 1716, 5148, 25740, 87516, 437580, 1662804, 8314020, 38244492, 167943204, 839716020, 3862693692, 17298150012, 86490750060, 397857450276, 1850902051284, 9254510256420, 42570747179532, 201748323589956, 1008741617949780, 4640211442568988

Offset: 1

Author

Reinhard Zumkeller, Jun 21 2011

Keywords

• nonn
• base

Comments

A050252(a(n)) = n and A050252(m) <> n for m < a(n);

Examples

			a(2) = 4 = 2^2 and A050252(12) = (1+1) = 2;
a(3) = 12 = 2^2 * 3 and A050252(12) = (1+1) + 1 = 3;
a(4) = 36 = 2^2 * 3^2 and A050252(36) = (1+1) + (1+1) = 4;
a(5) = 132 = 2^2 * 3 * 11 and A050252(132) = (1+1) + 1 + 2 = 5;
a(6) = 396 = 2^2 * 3^2 * 11 and A050252(396) = (1+1) + (1+1) + 2 = 6;
a(7) = 1716 = 2^2 * 3 * 11 * 13 and A050252(1716) = (1+1) + 1 + 2 + 2 = 7;
a(8) = 5148 = 2^2 * 3^2 * 11 * 13 and A050252(5148) = (1+1) + (1+1) + 2 + 2 = 8;
a(9) = 25740 = 2^2 * 3^2 * 5 * 11 * 13 and A050252(25740) = (1+1) + (1+1) + 1 + 2 + 2 = 9;
a(10) = 87516 = 2^2 * 3^2 * 11 * 13 * 17 and A050252(87516) = (1+1) + (1+1) + 2 + 2 + 2 = 10;
a(11) = 437580 = 2^2 * 3^2 * 5 * 11 * 13 * 17 and A050252(437580) = (1+1) + (1+1) + 1 + 2 + 2 + 2 = 11;
a(12) = 1662804 = 2^2 * 3^2 * 11 * 13 * 17 * 19 and A050252(1662804) = (1+1) + (1+1) + 2 + 2 + 2 + 2 = 12;
a(13) = 8314020 = 2^2 * 3^2 * 5 * 11 * 13 * 17 * 19 and A050252(8314020) = (1+1) + (1+1) + 1 + 2 + 2 + 2 + 2 = 13.
		

Programs

Haskell

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a192010 n = succ $ fromJust $ elemIndex n $ map a050252 [1..]

Extensions

a(14)-a(26) from Donovan Johnson, Jul 03 2011