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Search: id:A024528
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| A024528 |
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a(n) = n-th elementary symmetric function of {1, prime(1), prime(2), ..., prime(n-1)}. |
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+0
7
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| 1, 3, 11, 61, 457, 5237, 70391, 1226677, 23817373, 557499269, 16390571671, 514577415031, 19239924846277, 796257656832167, 34543329507310391, 1636619248175258407, 87355709935877186981, 5186576044693944076609
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(0) through a(12) are square-free. - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Sep 03 2004
For n>0 a(n) is the determinant of the n X n matrix with elements M[i,j] = 1+Prime[i] if i=j and 1 otherwise. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2006
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LINKS
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Eric Weisstein's World of Mathematics, Harmonic Series of Primes
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FORMULA
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A024528 are the numerators of the prime harmonic numbers + 1, i.e. a(n)/A002110(n) = Sum_i=0...n 1/p(i) where p(0) = 1, p(i) is the i-th prime for n > 0 and A002110 are the primorial numbers. - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Sep 03 2004
a(n) = Det[ DiagonalMatrix[ Table[ Prime[i], {i, 1, n} ] ] + 1 ]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2006
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MATHEMATICA
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Table[ Det[ DiagonalMatrix[ Table[ Prime[i], {i, 1, n} ] ] + 1 ], {n, 1, 20} ] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2006
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CROSSREFS
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Cf. A002110.
Sequence in context: A125556 A127516 A095237 this_sequence A004108 A069725 A096655
Adjacent sequences: A024525 A024526 A024527 this_sequence A024529 A024530 A024531
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Sep 09 2004
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