This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A099848 #16 May 13 2025 02:40:28
%S A099848 1,2,3,4,5,6,6,7,8,9,10,10,11,12,12,12,13,14,14,15,15,16,17,18,18,18,
%T A099848 19,20,20,20,21,21,22,22,23,24,24,24,24,25,26,26,27,28,28,28,29,30,30,
%U A099848 30,30,30,30,31,32,33,33,34,34,35,35,36,36,36,36,36,36,37,38,38,39,39,40
%N A099848 All natural numbers occur in their order as many times as they have ordered prime factorizations.
%C A099848 k occurs exactly once iff k is a prime power (A000961).
%C A099848 k occurs exactly twice iff k is a semiprime with distinct factors (A006881).
%H A099848 Reinhard Zumkeller, <a href="/A099848/b099848.txt">Table of n, a(n) for n = 1..10000</a>
%H A099848 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeFactorization.html">Prime Factorization</a>.
%F A099848 a(A099849(n) - k) = n for 0 <= k < A008480(n).
%e A099848 k = 12: A008480(12) = #{3*2*2, 2*3*2, 2*2*3} = 3, therefore 12 occurs three times.
%t A099848 Table[n, {n, 1, 40}, {Multinomial @@ FactorInteger[n][[;; , 2]]}] // Flatten (* _Amiram Eldar_, May 13 2025 *)
%o A099848 (Haskell)
%o A099848 a099848 n = a099848_list !! (n-1)
%o A099848 a099848_list = concat $ zipWith replicate a008480_list [1..]
%o A099848 -- _Reinhard Zumkeller_, Nov 19 2015
%Y A099848 Cf. A000961, A006881, A008480, A099849.
%K A099848 nonn,easy
%O A099848 1,2
%A A099848 _Reinhard Zumkeller_, Oct 27 2004