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%I #22 Nov 15 2019 08:08:27
%S 1,10,55,192,522,1197,2432,4520,7838,12867,20193,30524,44696,63694,
%T 88658,120895,161885,213294,276997,355082,449849,563834,699826,860861,
%U 1050260,1271598,1528765,1825937,2167611,2558606,3004075,3509523
%N Number of positive integers <= 10^n that are divisible by no prime exceeding 11.
%C Lehmer quotes A. E. Western as computing a(5) = 1197, a(8) = 7838 and a(10) = 20193.
%C Number of integers of the form 2^a*3^b*5^c*7^d*11^e <= 10^n.
%H David A. Corneth, <a href="/A107352/b107352.txt">Table of n, a(n) for n = 0..119</a>
%H 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 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 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 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 *)
%Y Row 5 of A253635.
%Y Cf. A011557, A051038.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, May 23 2005
%E More terms from _Robert G. Wilson v_ and _Don Reble_, May 26 2005
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