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%I #19 Apr 15 2021 05:25:01
%S 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 18,19,19,20,20,21,22,23,23,24,25,26,26,27,28,29,30,30,31,32,32,32,32,
%U 33,34,35,35,36,36,37,38,39,39,40,41,41,41,42,43,44,45
%N a(n) is the number of not-sqrt-smooth numbers ("jagged" numbers) not exceeding n. This is the counting function of A064052.
%C This sequence is different from shifted A072490, after 22 terms.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 166.
%D Daniel H. Greene and Donald E. Knuth, Mathematics for the Analysis of Algorithms, 3rd ed., Birkhäuser, 1990, pp. 95-98.
%F From _Ridouane Oudra_, Nov 07 2019: (Start)
%F a(n) = Sum_{i=1..floor(sqrt(n))} (pi(floor(n/i)) - pi(i)).
%F a(n) = Sum_{p<=sqrt(n)} (p-1) + Sum_{sqrt(n)<p<=n} floor(n/p), where p is prime.
%F a(n) = n - A064775(n). (End)
%F 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 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}]
%Y Cf. A064052, A064775, A072490, A153810, A242610.
%K nonn
%O 1,3
%A _Jean-François Alcover_, May 16 2014
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