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Search: id:A069933
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| A069933 |
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Number of k, 1<=k<=n, such that core(k) divides n, where core(x) is the square-free part of x, the smallest integer such that x*core(x) is a square. |
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+0
1
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| 1, 2, 2, 3, 3, 5, 3, 4, 4, 7, 4, 8, 4, 7, 7, 6, 5, 10, 5, 10, 8, 9, 5, 11, 7, 10, 8, 11, 6, 18, 6, 9, 10, 11, 10, 15, 7, 12, 11, 14, 7, 20, 7, 13, 13, 12, 7, 16, 9, 17, 13, 15, 8, 19, 13, 16, 13, 14, 8, 27, 8, 14, 15, 13, 14, 25, 9, 16, 14, 25, 9, 21, 9, 16, 18, 17, 14, 27, 9, 20, 14, 17
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sequence does not give the number of all integers of the form core(k) dividing n since this set is infinite (for any square x^2 core(x^2)=1 divides n).
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FORMULA
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Asymptotically (still conjectured) : sum(k=1, n, a(k))=n^C+O(n^C) with C=1, 54...
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PROGRAM
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(PARI) for(n=1, 150, print1(sum(i=1, n, if(n%core(i), 0, 1)), ", "))
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CROSSREFS
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Sequence in context: A060749 A138305 A079375 this_sequence A102347 A069974 A039650
Adjacent sequences: A069930 A069931 A069932 this_sequence A069934 A069935 A069936
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), May 05 2002
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