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A024528 a(n) = n-th elementary symmetric function of {1, prime(1), prime(2), ..., prime(n)}. 8
1, 3, 11, 61, 457, 5237, 70391, 1226677, 23817373, 557499269, 16390571671, 514577415031, 19239924846277, 796257656832167, 34543329507310391, 1636619248175258407, 87355709935877186981, 5186576044693944076609 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(0) through a(12) are squarefree. - Gerald McGarvey, 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, Jun 02 2006

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..500

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, Sep 03 2004

a(n) = Det[ DiagonalMatrix[ Table[ Prime[i], {i, 1, n} ] ] + 1 ]. - Alexander Adamchuk, Jun 02 2006

a(0) = 1, a(n) = A000040(n)*a(n-1) + A002110(n-1) for n>=1. - Philippe Deléham, Jun 03 2015

EXAMPLE

a(0) = 1

a(1) = 1*2 + A002110(0) = 2 + 1 = 3

a(2) = 3*3 + A002110(1) = 9 + 2 = 11

a(3) = 11*5 + A002110(2) = 55 + 6 = 61

a(4) = 61*7 + A002110(3) = 427 + 30 = 457

a(5) = 457*11 + A002110(4) = 5027 + 210 = 5237

a(6) = 5237*13 + A002110(5) = 68081 + 2310 = 70391

a(7) = 70391*17 + A002110(6) = 1196647 + 30030 = 1226677 - Philippe Deléham, Jun 03 2015

MAPLE

N:= 30: # to get a(0) to a(N)

Primes:= [seq(ithprime(i), i=1..N)]:

seq(mul(Primes[i], i=1..n)*(1+add(1/Primes[i], i=1..n)), n=0..N); # Robert Israel, Jun 03 2015

MATHEMATICA

Table[ Det[ DiagonalMatrix[ Table[ Prime[i], {i, 1, n} ] ] + 1 ], {n, 1, 20} ] (* Alexander Adamchuk, Jun 02 2006 *)

p[0] = 1; p[n_] := Prime[n];

t[n_] := Table[p[k], {k, 0, n}]

a[n_] := SymmetricPolynomial[n, t[n]]

Table[a[n], {n, 0, 20}]

(* Clark Kimberling, Aug 18 2012 *)

CROSSREFS

Cf. A000040, A002110, A024451.

Sequence in context: A228204 A095237 A185385 * A273468 A004108 A203007

Adjacent sequences:  A024525 A024526 A024527 * A024529 A024530 A024531

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from T. D. Noe, Sep 09 2004

STATUS

approved

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Last modified January 19 20:33 EST 2019. Contains 319310 sequences. (Running on oeis4.)