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Search: id:A107352
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| A107352 |
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Number of positive integers <= 10^n that are divisible by no prime exceeding 11. |
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+0
2
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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.
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REFERENCES
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D. H. Lehmer, The lattice points of an n-dimensional tetrahedron, Duke Math. J., 7 (1941), 341-353.
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MATHEMATICA
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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}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 24 2005)
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CROSSREFS
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Sequence in context: A119334 A074977 A069155 this_sequence A127761 A070212 A008502
Adjacent sequences: A107349 A107350 A107351 this_sequence A107353 A107354 A107355
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 23 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and Don Reble (djr(AT)nk.ca), May 26 2005
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