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Search: id:A081239
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| A081239 |
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#{(i,j): mu(i)*mu(j) = 0, 1<=i,j<=n}, where mu=A008683 (Moebius function). |
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+0
3
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| 0, 0, 0, 7, 9, 11, 13, 28, 45, 51, 57, 80, 88, 96, 104, 135, 145, 180, 192, 231, 245, 259, 273, 320, 369, 387, 440, 495, 517, 539, 561, 624, 648, 672, 696, 767, 793, 819, 845, 924, 952, 980, 1008, 1095, 1184, 1216, 1248, 1343, 1440, 1539, 1577, 1680, 1720
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OFFSET
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1,4
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COMMENT
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A081238(n) + a(n) + A081240(n) = n^2;
a(n) = a(n-1) + 2*n + 1 iff mu(n) = 0.
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FORMULA
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a(n) = n^2 - A013928(n+1)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 12 2003
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EXAMPLE
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n mu(n) ... n: 1 2 3 4 5 6 7 8
- ------ .... |----------------
1 .. +1 ..... | + - - 0 - + - 0
2 .. -1 ..... | - + + 0 + - + 0
3 .. -1 ..... | - + + 0 + - + 0
4 ... 0 ..... | 0 0 0 0 0 0 0 0
5 .. -1 ..... | - + + 0 + - + 0 a(8)=28, as there are
6 .. +1 ..... | + - - 0 - + - 0 28 '0's in the 8x8-square
7 .. -1 ..... | - + + 0 + - + 0
8 ... 0 ..... | 0 0 0 0 0 0 0 0.
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CROSSREFS
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Cf. A057627.
Sequence in context: A162018 A055741 A103621 this_sequence A029612 A120165 A024828
Adjacent sequences: A081236 A081237 A081238 this_sequence A081240 A081241 A081242
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 11 2003
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