A188584 - OEIS

A188584

Numerator in first column of matrix exponential of A175992.

1, 1, 1, 3, 1, 2, 1, 13, 3, 2, 1, 7, 1, 2, 2, 73, 1, 7, 1, 7, 2, 2, 1, 17, 3, 2, 13, 7, 1, 5, 1, 167, 2, 2, 2, 27, 1, 2, 2, 17, 1, 5, 1, 7, 7, 2, 1, 209, 3, 7, 2, 7, 1, 17, 2, 17, 2, 2, 1, 10, 1, 2, 7, 4051, 2, 5, 1, 7, 2, 5, 1, 47, 1, 2, 7, 7, 2, 5, 1, 209, 73, 2, 1, 10, 2, 2, 2, 17, 1, 10, 2, 7, 2, 2, 2

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OFFSET

1,4

COMMENTS

Numerator in first column of exp(M) = Sum_{n>=0} M^n/n! where M is the triangular matrix given as A175992.

The Dirichlet series that generates the fraction A188584/A188583 is A001113^(Riemann zeta function - 1).

LINKS

Table of n, a(n) for n=1..95.

PROG

(PARI)

A175992(n, k)=if(k==n, 0, if(n%k==0, 1, 0));

N=40; /* that many terms */

M=matrix(N, N, r, c, A175992(r, c) );

E=sum(j=0, N, M^j/j!); /* matrix exponential */

c1=E[, 1]; /* first column */

vector(N, j, numerator(c1[j])) /* show terms */ /* Joerg Arndt, Apr 16 2011 */

CROSSREFS

Sequence in context: A321889 A321751 A364906 * A103514 A324123 A016570

Adjacent sequences: A188581 A188582 A188583 * A188585 A188586 A188587

KEYWORD

nonn,frac

AUTHOR

Mats Granvik, Apr 04 2011

EXTENSIONS

Sequence terms added, title changed, and comment lines changed by Mats Granvik, Apr 14 2011

STATUS

approved