OFFSET
1,3
COMMENTS
a(n) = the coefficient of x^d(n) in the product: Product_{k=1..n} (1 + x^d(k)).
EXAMPLE
The first 10 terms of the number-of-divisors sequence (A000005) are 1,2,2,3,2,4,2,4,3,4. For a(10), we want the number of partitions of these 10 terms that sum to d(10)=4. We have: d(10)=4, d(8)=4, d(6)=4, d(9)+d(1) = 3+1, d(4)+d(1) = 3+1, d(7)+d(5) = d(7)+d(3) = d(7)+d(2) = d(5)+d(3) = d(5)+d(2) = d(3)+d(2) = 2+2. So there are 11 such sums (including those equal to 4 itself). Therefore a(10)=11.
MAPLE
A175108 := proc(n) g := 1 ; for k from 1 to n do g := g*(1+x^numtheory[tau](k)) ; g := expand(g) ; end do ; coeftayl(g, x=0, numtheory[tau](n)) ; end proc: seq(A175108(n), n=1..80) ; # R. J. Mathar, Mar 05 2010
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Feb 12 2010
EXTENSIONS
More terms from R. J. Mathar and Ray Chandler, Mar 05 2010
STATUS
approved