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A010846
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Number of numbers <= n whose prime factors are a subset of prime factors of n.
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3
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1, 2, 2, 3, 2, 5, 2, 4, 3, 6, 2, 8, 2, 6, 5, 5, 2, 10, 2, 8, 5, 7, 2, 11, 3, 7, 4, 8, 2, 18, 2, 6, 6, 8, 5, 14, 2, 8, 6, 11, 2, 19, 2, 9, 8, 8, 2, 15, 3, 12, 6, 9, 2, 16, 5, 11, 6, 8, 2, 26, 2, 8, 8, 7, 5, 22, 2, 10, 6, 20, 2, 18, 2, 9, 9, 10, 5, 23, 2, 14, 5, 9, 2, 28, 5, 9, 7, 11, 2, 32, 5, 10
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This function of n appears in an ABC-conjecture by Andrew Granville. See Goldfeld. [From T. D. Noe (noe(AT)sspectra.com), Jun 30 2009]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..5000
Dorian Goldfled, Modular Forms, Elliptic Curves, and the ABC Conjecture [From T. D. Noe (noe(AT)sspectra.com), Jun 30 2009]
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FORMULA
| a(n=\prod {p_k}^{r_k} )= \#\{x=\prod {p_i}^{t_i} <=n | \prod p_i {\rm divides }\prod p_k\}.
a(n) = |{k<=n, k|n^(tau(k)-1)}|. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 13 2006
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MATHEMATICA
| pf[n_] := If[n==1, {}, Transpose[FactorInteger[n]][[1]]]; SubsetQ[lst1_, lst2_] := Intersection[lst1, lst2]==lst1; Table[pfn=pf[n]; Length[Select[Range[n], SubsetQ[pf[ # ], pfn] &]], {n, 100}] [From T. D. Noe (noe(AT)sspectra.com), Jun 30 2009]
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CROSSREFS
| A162306 (numbers for each n) [From T. D. Noe (noe(AT)sspectra.com), Jun 30 2009]
Sequence in context: A033099 A018892 A100565 * A073023 A173754 A180125
Adjacent sequences: A010843 A010844 A010845 * A010847 A010848 A010849
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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