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 A383397 #24 Apr 29 2025 12:41:49
%S A383397 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,25,26,27,28,
%T A383397 29,30,31,32,33,34,35,36,37,38,39,41,42,43,44,46,47,49,50,51,52,53,54,
%U A383397 55,57,58,59,61,62,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,81,82,83,85,86,87,88,89,91,92,93,94,95,97,98,99,100,101
%N A383397 Numbers in whose canonical prime factorization the powers of the primes form a strictly increasing sequence.
%C A383397 Alternative name: positive integers with canonical prime factorization p_1 ^ e_1 * p_2 ^ e_2 * ... * p_k ^ e_k which satisfy p_1 ^ e_1 < p_2 ^ e_2 < ... < p_k ^ e_k.
%C A383397 The asymptotic density of this sequence seems to be about 0.84.
%H A383397 Boas Bakker, <a href="/A383397/b383397.txt">Table of n, a(n) for n = 1..100000</a>
%e A383397 18 = 2^1 * 3^2 is in the sequence as 2^1 < 3^2.
%e A383397 12 is not in the sequence because 12 = 2^2 * 3^1 and 4>3.
%t A383397 Select[Range[100], Less @@ Power @@@ FactorInteger[#] &] (* _Amiram Eldar_, Apr 26 2025 *)
%o A383397 (PARI) is(n) = {my(f = factor(n), r = 0); for(i = 1, #f~, c = f[i,1]^f[i,2]; if(c > r, r = c, return(0))); 1} \\ _David A. Corneth_, Apr 26 2025
%Y A383397 Complement of A140831.
%Y A383397 Cf. A005117.
%K A383397 nonn,easy
%O A383397 1,2
%A A383397 _Boas Bakker_, Apr 26 2025