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A107352 Number of positive integers <= 10^n that are divisible by no prime exceeding 11.

%I A107352 #26 Oct 23 2024 00:42:54
%S A107352 1,10,55,192,522,1197,2432,4520,7838,12867,20193,30524,44696,63694,
%T A107352 88658,120895,161885,213294,276997,355082,449849,563834,699826,860861,
%U A107352 1050260,1271598,1528765,1825937,2167611,2558606,3004075,3509523
%N A107352 Number of positive integers <= 10^n that are divisible by no prime exceeding 11.
%C A107352 Lehmer quotes A. E. Western as computing a(5) = 1197, a(8) = 7838 and a(10) = 20193.
%C A107352 Number of integers of the form 2^a*3^b*5^c*7^d*11^e <= 10^n.
%H A107352 David A. Corneth, <a href="/A107352/b107352.txt">Table of n, a(n) for n = 0..119</a>
%H A107352 D. H. Lehmer, <a href="https://doi.org/10.1215/S0012-7094-40-00719-0">The lattice points of an n-dimensional tetrahedron</a>, Duke Math. J., 7 (1941), 341-353.
%F A107352 Does a(n)/(a(n-1) - a(n-2)) tend to c*n + d for large n where c ~= 0.20 and d ~= 1.37? - _David A. Corneth_, Nov 14 2019
%t A107352 fQ[n_] := FactorInteger[n][[ -1, 1]] < 13; c = 1; k = 1; Do[ While[k <= 10^n, If[ fQ[k], c++ ]; k++ ]; Print[c], {n, 0, 9}] (* Or *)
%t A107352 n = 32; t = Select[ Flatten[ Table[11^e*Select[ Flatten[ Table[7^d*Select[ Flatten[ Table[5^c*Select[ Flatten[ Table[2^a*3^b, {a, 0, Log[2, 10^n]}, {b, 0, Log[3, 10^n]}]], # <= 10^n &], {c, 0, Log[5, 10^n]}]], # <= 10^n &], {d, 0, Log[7, 10^n]}]], # <= 10^n &], {e, 0, Log[11, 10^n]}]], # <= 10^n &]; Table[ Length[ Select[t, # <= 10^n &]], {n, 0, 32}] (* _Robert G. Wilson v_, May 24 2005 *)
%o A107352 (Python)
%o A107352 from sympy import integer_log, prevprime
%o A107352 def A107352(n):
%o A107352     def g(x, m): return sum((x//3**i).bit_length() for i in range(integer_log(x, 3)[0]+1)) if m==3 else sum(g(x//(m**i), prevprime(m))for i in range(integer_log(x, m)[0]+1))
%o A107352     return g(10**n,11) # _Chai Wah Wu_, Oct 22 2024
%Y A107352 Row 5 of A253635.
%Y A107352 Cf. A011557, A051038.
%K A107352 nonn
%O A107352 0,2
%A A107352 _N. J. A. Sloane_, May 23 2005
%E A107352 More terms from _Robert G. Wilson v_ and _Don Reble_, May 26 2005