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A160014
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Generalized Clausen numbers (table read by antidiagonals.)
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6
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1, 1, 1, 2, 2, 1, 3, 6, 3, 1, 2, 2, 3, 1, 1, 5, 30, 15, 5, 5, 1, 6, 2, 3, 1, 5, 1, 1, 7, 42, 21, 35, 35, 7, 7, 1, 2, 2, 15, 1, 5, 1, 7, 1, 1, 3, 30, 3, 5, 5, 7, 7, 1, 1, 1, 10, 2, 3, 1, 35, 1, 7, 1, 1, 1, 1, 11, 66, 165, 385, 55, 77, 77, 11, 11, 11, 11, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| T(n,k) = Product_{ p - k | n} p, where p is prime.
T(n,0) is the squarefree kernel of n (A007947).
T(n,1) are the classical Clausen numbers (A141056). The classical Clausen numbers are by the von Staudt-Clausen theorem the denominators of the Bernoulli numbers.
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REFERENCES
| Clausen, Thomas, "Lehrsatz aus einer Abhandlung ueber die Bernoullischen Zahlen", Astr. Nachr. 17 (1840), 351-352.
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EXAMPLE
| [k\n][0--1--2---3---4---5---6---7----8----9---10---11----12---13---14----15]
[0]...1..1..2...3...2...5...6...7....2....3...10...11.....6...13...14....15
[1]...1..2..6...2..30...2..42...2...30....2...66....2..2730....2....6.....2
[2]...1..3..3..15...3..21..15...3....3..165...21...39....15....3....3..1785
[3]...1..1..5...1..35...1...5...1..385....1...65....1....35....1...85.....1
[4]...1..5..5..35...5...5..35..55....5..455....5....5....35...85...55...665
[5]...1..1..7...1...7...1..77...1...91....1....7....1..1309....1..133.....1
T(3,4) = 35 = 5*7 because 5 and 7 are the only prime numbers p such that
(p - 4) divides 3.
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MAPLE
| Clausen := proc(n, k) local S, i;
S := numtheory[divisors](n);
S := map(i->i+k, S);
S := select(isprime, S);
mul(i, i=S) end:
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CROSSREFS
| Cf. A141056, A027760, A027642
Sequence in context: A080955 A125231 A117919 * A068956 A124842 A134399
Adjacent sequences: A160011 A160012 A160013 * A160015 A160016 A160017
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KEYWORD
| nonn
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Apr 29 2009
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EXTENSIONS
| Swapped n<>k fixed by Peter Luschny (peter(AT)luschny.de), May 04 2009
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