cp's OEIS Frontend

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

%I A192010 #12 Mar 30 2012 18:51:10
%S A192010 1,4,12,36,132,396,1716,5148,25740,87516,437580,1662804,8314020,
%T A192010 38244492,167943204,839716020,3862693692,17298150012,86490750060,
%U A192010 397857450276,1850902051284,9254510256420,42570747179532,201748323589956,1008741617949780,4640211442568988
%N A192010 The smallest number with n digits in its prime factorization (total count of digits of all bases and exponents).
%C A192010 A050252(a(n)) = n and A050252(m) <> n for m < a(n);
%e A192010 a(2) = 4 = 2^2 and A050252(12) = (1+1) = 2;
%e A192010 a(3) = 12 = 2^2 * 3 and A050252(12) = (1+1) + 1 = 3;
%e A192010 a(4) = 36 = 2^2 * 3^2 and A050252(36) = (1+1) + (1+1) = 4;
%e A192010 a(5) = 132 = 2^2 * 3 * 11 and A050252(132) = (1+1) + 1 + 2 = 5;
%e A192010 a(6) = 396 = 2^2 * 3^2 * 11 and A050252(396) = (1+1) + (1+1) + 2 = 6;
%e A192010 a(7) = 1716 = 2^2 * 3 * 11 * 13 and A050252(1716) = (1+1) + 1 + 2 + 2 = 7;
%e A192010 a(8) = 5148 = 2^2 * 3^2 * 11 * 13 and A050252(5148) = (1+1) + (1+1) + 2 + 2 = 8;
%e A192010 a(9) = 25740 = 2^2 * 3^2 * 5 * 11 * 13 and A050252(25740) = (1+1) + (1+1) + 1 + 2 + 2 = 9;
%e A192010 a(10) = 87516 = 2^2 * 3^2 * 11 * 13 * 17 and A050252(87516) = (1+1) + (1+1) + 2 + 2 + 2 = 10;
%e A192010 a(11) = 437580 = 2^2 * 3^2 * 5 * 11 * 13 * 17 and A050252(437580) = (1+1) + (1+1) + 1 + 2 + 2 + 2 = 11;
%e A192010 a(12) = 1662804 = 2^2 * 3^2 * 11 * 13 * 17 * 19 and A050252(1662804) = (1+1) + (1+1) + 2 + 2 + 2 + 2 = 12;
%e A192010 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.
%o A192010 (Haskell)
%o A192010 import Data.List (elemIndex)
%o A192010 import Data.Maybe (fromJust)
%o A192010 a192010 n = succ $ fromJust $ elemIndex n $ map a050252 [1..]
%K A192010 nonn,base
%O A192010 1,2
%A A192010 _Reinhard Zumkeller_, Jun 21 2011
%E A192010 a(14)-a(26) from _Donovan Johnson_, Jul 03 2011