|
| |
|
|
A024528
|
|
a(n) = n-th elementary symmetric function of {1, prime(1), prime(2), ..., prime(n-1)}.
|
|
8
| |
|
|
1, 3, 11, 61, 457, 5237, 70391, 1226677, 23817373, 557499269, 16390571671, 514577415031, 19239924846277, 796257656832167, 34543329507310391, 1636619248175258407, 87355709935877186981, 5186576044693944076609
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| a(0) through a(12) are squarefree. - 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
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Harmonic Series of Primes
|
|
|
FORMULA
| 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
|
|
|
MATHEMATICA
| Table[ Det[ DiagonalMatrix[ Table[ Prime[i], {i, 1, n} ] ] + 1 ], {n, 1, 20} ] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 02 2006
|
|
|
CROSSREFS
| Cf. A002110.
Sequence in context: A127516 A095237 A185385 * A004108 A203007 A203768
Adjacent sequences: A024525 A024526 A024527 * A024529 A024530 A024531
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
|
|
|
EXTENSIONS
| More terms from T. D. Noe (noe(AT)sspectra.com), Sep 09 2004
|
| |
|
|
