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Search: id:A139547
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| A139547 |
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Square array of lcm sequences read by upwards antidiagonals, in which row products give the factorials. |
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+0
5
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| 1, 1, 1, 2, 1, 1, 6, 1, 1, 1, 12, 1, 1, 1, 1, 60, 2, 1, 1, 1, 1, 60, 2, 1, 1, 1, 1, 1, 420, 6, 1, 1, 1, 1, 1, 1, 840, 6, 2, 1, 1, 1, 1, 1, 1, 2520, 12, 2, 1, 1, 1, 1, 1, 1, 1, 2520, 12, 2, 1, 1, 1, 1, 1, 1, 1, 1, 27720, 60, 6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 27720, 60, 6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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This table seems to fit the formula of I. Vardi given in equation (11) in the Mathworld section about the von Mangoldt Function. The first columns are A003418, A139550, A139552, A139554.
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REFERENCES
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A. Granville and G. Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), p. 10-11.
I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 155.
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LINKS
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Weisstein, Eric W, Mangoldt Function..
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FORMULA
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T(n,k) = if n>=k then A003418((A120885-1)) else 1.
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EXAMPLE
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Beginning of array and row products:
1 1 1 1 1 1 1 1 1 ... = 1
1 1 1 1 1 1 1 1 1 ... = 1
2 1 1 1 1 1 1 1 1 ... = 2
6 1 1 1 1 1 1 1 1 ... = 6
12 2 1 1 1 1 1 1 1 ... = 24
60 2 1 1 1 1 1 1 1 ... = 120
60 6 2 1 1 1 1 1 1 ... = 720
420 6 2 1 1 1 1 1 1 ... = 5040
840 12 2 2 1 1 1 1 1 ... = 40320
...
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CROSSREFS
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Cf. A000142, A014963, A003418, A139550, A139552, A139554.
Cf. A120885.
Adjacent sequences: A139544 A139545 A139546 this_sequence A139548 A139549 A139550
Sequence in context: A036563 A025264 A139622 this_sequence A096162 A053383 A125731
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KEYWORD
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nonn,tabl
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AUTHOR
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Mats O. Granvik (mgranvik(AT)abo.fi), Apr 27 2008, May 07 2008
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