A108465 Table read by antidiagonals: T(n,k) (n>=2) = number of factorizations of (n,k) into pairs (i,j) with i,j>1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 3, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 4, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1

Offset

2,13

Comments

(a,b)*(x,y)=(a*x,b*y).

Links

Table of n, a(n) for n=2..106.

Formula

Dirichlet g.f.: A(s, t) = exp(B(s, t)/1 + B(2*s, 2*t)/2 + B(3*s, 3*t)/3 + ...) where B(s, t) = (zeta(s)-1)*(zeta(t)-1).

Example

1 1 1 1 1 ...
1 1 1 1 1 ...
1 1 2 1 2 ...
1 1 1 1 1 ...
1 1 2 1 3 ...
(8,6)=(4,3)*(2,2)=(4,2)*(2,3), so a(8,6)=3.

Crossrefs

Cf. A108461. Columns 4, 6: A038548 (n>1), A032741. Main diagonal: A108466.

Sequence in context: A350040 A280940 A131789 * A367419 A069347 A161606

Adjacent sequences: A108462 A108463 A108464 * A108466 A108467 A108468

Keyword

nonn,tabl

Author

Christian G. Bower, Jun 03 2005

Status

approved