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A107352 Number of positive integers <= 10^n that are divisible by no prime exceeding 11. 5
1, 10, 55, 192, 522, 1197, 2432, 4520, 7838, 12867, 20193, 30524, 44696, 63694, 88658, 120895, 161885, 213294, 276997, 355082, 449849, 563834, 699826, 860861, 1050260, 1271598, 1528765, 1825937, 2167611, 2558606, 3004075, 3509523 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Lehmer quotes A. E. Western as computing a(5) = 1197, a(8) = 7838 and a(10) = 20193.

Number of integers of the form 2^a*3^b*5^c*7^d*11^e <= 10^n.

LINKS

David A. Corneth, Table of n, a(n) for n = 0..119

D. H. Lehmer, The lattice points of an n-dimensional tetrahedron, Duke Math. J., 7 (1941), 341-353.

FORMULA

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

MATHEMATICA

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 *)

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 *)

CROSSREFS

Row 5 of A253635.

Cf. A011557, A051038.

Sequence in context: A321780 A074977 A069155 * A127761 A244871 A162617

Adjacent sequences:  A107349 A107350 A107351 * A107353 A107354 A107355

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 23 2005

EXTENSIONS

More terms from Robert G. Wilson v and Don Reble, May 26 2005

STATUS

approved

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Last modified May 27 18:56 EDT 2020. Contains 334664 sequences. (Running on oeis4.)