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

1,2

Comments

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

Links

Table of n, a(n) for n=1..26.

Example

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.

Prog

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

Crossrefs

Sequence in context: A113990 A231179 A331717 * A252697 A056383 A293857

Adjacent sequences: A192007 A192008 A192009 * A192011 A192012 A192013

Keyword

nonn,base

Author

Reinhard Zumkeller, Jun 21 2011

Extensions

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

Status

approved