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Search: id:A070829
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| A070829 |
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Array showing which primes divide n>=2. |
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+0
1
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| 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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In the Kac reference this array is called rho_{p}(n) := 1 if p divides n else 0.
The row length sequence is A061395(n),n>=2: [1,2,1,3,2,4,1,2,3,5,2,6,4,3,...] (the index of the largest prime dividing n). All row entries beyond these numbers are 0, hence they are not shown. The n=1 row would have 0 for all entries.
The column sequences (without leading zeros) give for m>=1 periodic sequences with the period: 1 followed by p(m)-1 zeros. They start with n=p(m) := A000040(m).
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REFERENCES
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Mark Kac, A Personal History of the Scottish Book, pp. 17-27, in R. D. Mauldin (edt.), The Scottish Book, Birkhaeuser, Boston, Basel, 1981.
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LINKS
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W. Lang, First 32 rows.
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FORMULA
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a(n, m)=1 if p(m), m>=1, divides n>=2, with the prime p(m) := A000040(m), else 0.
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EXAMPLE
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{1}, {0, 1}, {1}, {0, 0, 1}, {1, 1}, {0, 0, 0, 1}, {1}, {0, 1}, {1, 0, 1}...
Row n=10: {1,0,1} because p(1)=2 and p(3)= 5 divides 10.
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CROSSREFS
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Cf. A067255 (array with multiplicities).
Sequence in context: A141212 A137893 A108882 this_sequence A118175 A120526 A086694
Adjacent sequences: A070826 A070827 A070828 this_sequence A070830 A070831 A070832
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 17, 2002
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