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Search: id:A125728
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| A125728 |
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a(n) = sum{k=1 to n}(number of positive integers <=k which are coprime to both k and n). |
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+0
2
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| 1, 2, 4, 5, 10, 7, 18, 16, 23, 19, 42, 24, 58, 38, 46, 56, 96, 52, 120, 72, 93, 93, 172, 91, 171, 132, 176, 143, 270, 116, 308, 218, 237, 228, 280, 201, 432, 286, 330, 275, 530, 237, 584, 368, 394, 417, 696, 357, 666, 431, 570, 515, 882, 452, 716, 565, 712, 665
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equals row sums of triangle A144379 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 19 2008]
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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a(n) = sum{j=1 to n} sum{k|(n*j)} mu(k) * floor(j/k), where mu(k) is the Mobius (Moebius) function and the inner sum is over the positive divisors, k, of (n*j).
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EXAMPLE
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The positive integers coprime to k and <= k are, as k runs from 1 to 8, 1; 1; 1,
2; 1,3; 1,2,3,4; 1,5; 1,2,3,4,5,6; 1,3,5,7. So we want, so as to
get a(8), the number of 1's, 3's, 5's and 7's in this concatenated
list, since the positive integers <=8 and coprime to 8 are 1,3,5,
7. In the concatenated list there are eight 1's, four 3's, three
5's and one 7. So a(8) = 8+4+3+1 = 16.
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MATHEMATICA
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f[n_] := Sum[Sum[ Boole[GCD[j, k] == 1 && GCD[j, n] == 1], {j, k}], {k, n}]; Table[f[n], {n, 60}] (*Chandler*)
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CROSSREFS
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A144379 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 19 2008]
Adjacent sequences: A125725 A125726 A125727 this_sequence A125729 A125730 A125731
Sequence in context: A067298 A077389 A122991 this_sequence A156799 A003278 A004792
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Feb 02 2007
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 03 2007
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