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 A242493 #23 Sep 01 2024 10:42:45
%S A242493 0,1,2,2,3,4,5,5,5,6,7,7,8,9,10,10,11,11,12,13,14,15,16,16,16,17,17,
%T A242493 18,19,19,20,20,21,22,23,23,24,25,26,26,27,28,29,30,30,31,32,32,32,32,
%U A242493 33,34,35,35,36,36,37,38,39,39,40,41,41,41,42,43,44,45
%N A242493 a(n) is the number of not-sqrt-smooth numbers ("jagged" numbers) not exceeding n. This is the counting function of A064052.
%C A242493 This sequence is different from shifted A072490, after 22 terms.
%D A242493 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 166.
%D A242493 Daniel H. Greene and Donald E. Knuth, Mathematics for the Analysis of Algorithms, 3rd ed., Birkhäuser, 1990, pp. 95-98.
%F A242493 From _Ridouane Oudra_, Nov 07 2019: (Start)
%F A242493 a(n) = Sum_{i=1..floor(sqrt(n))} (pi(floor(n/i)) - pi(i)).
%F A242493 a(n) = Sum_{p<=sqrt(n)} (p-1) + Sum_{sqrt(n)<p<=n} floor(n/p), where p is prime.
%F A242493 a(n) = n - A064775(n). (End)
%F A242493 a(n) ~ log(2)*n - A153810 * n/log(n) - A242610 * n/log(n)^2 + O(n/log(n)^3) (Greene and Knuth, 1990). - _Amiram Eldar_, Apr 15 2021
%t A242493 jaggedQ[n_] := jaggedQ[n] = (f = FactorInteger[n][[All, 1]]; s = Sqrt[n]; Count[f, p_ /; p > s] > 0); a[n_] := ( For[ cnt = 0; j = 2, j <= n, j++, If[jaggedQ[j], cnt++]]; cnt); Table[a[n], {n, 1, 100}]
%o A242493 (Python)
%o A242493 from math import isqrt
%o A242493 from sympy import primepi
%o A242493 def A242493(n): return sum(primepi(n//i)-primepi(i) for i in range(1,isqrt(n)+1)) # _Chai Wah Wu_, Sep 01 2024
%Y A242493 Cf. A064052, A064775, A072490, A153810, A242610.
%K A242493 nonn
%O A242493 1,3
%A A242493 _Jean-François Alcover_, May 16 2014