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A084884
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Triangular array, read by rows: T(n,k) = numerator of arithmetic derivative of n/k, 1<=k<=n.
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3
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0, 1, 0, 1, -1, 0, 4, 1, 8, 0, 1, -3, -2, -1, 0, 5, 1, 1, -1, 19, 0, 1, -5, -4, -3, -2, -29, 0, 12, 4, 28, 1, 52, 8, 76, 0, 6, 3, 1, -3, 21, -1, 33, -15, 0, 7, 1, 11, -3, 1, -2, 39, -1, 1, 0, 1, -9, -8, -5, -6, -49, -4, -31, -19, -67, 0, 16, 5, 4, 1, 68, 1, 100, -1, 8, 19, 164
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| Arithmetic derivative of n/k = (k*A003415(n)-n*A003415(k))/k^2;
T(n,1) = A003415(n); T(n,n) = 0.
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LINKS
| Eric Weisstein's World of Mathematics, Quotient Rule.
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EXAMPLE
| ......................... 0
................... 1 ........ 0
............... 1 .... -1/4 ....... 0
........... 4 ..... 1 ...... 8/9 ....... 0
....... 1 ... -3/4 ... -2/9 ...... -1 ...... 0
... 5 ..... 1 ..... 1 ..... -1/4 .... 19/25 .... 0
1 .. -5/4 ... -4/9 ... -3/2 ... -2/25 ... -29/36 ... 0.
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CROSSREFS
| Denominator=A084885, A084886, A084890.
Sequence in context: A193842 A134250 A139045 * A143320 A089146 A101512
Adjacent sequences: A084881 A084882 A084883 * A084885 A084886 A084887
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KEYWORD
| sign,tabl
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 10 2003
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