

A175108


a(n) = number of partitions of d(n) into d(k)'s, where the k's are each <= n and distinct, but the d(k)'s need not be distinct. Here d(m) = the number of divisors of m.


1



1, 1, 2, 3, 3, 5, 4, 9, 6, 11, 5, 37, 6, 21, 22, 33, 7, 88, 8, 117, 36, 37, 9, 533, 12, 47, 48, 200, 10, 898, 11, 306, 68, 69, 70, 2124, 12, 82, 83, 1864, 13, 2298, 14, 612, 613, 109, 15, 14892, 19, 755, 125, 771, 16, 4669, 141, 4810, 142, 143, 17, 120808, 18, 177, 1265
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OFFSET

1,3


COMMENTS

a(n) = the coefficient of x^d(n) in the product: Product_{k=1..n} (1 + x^d(k)).


LINKS

Table of n, a(n) for n=1..63.


EXAMPLE

The first 10 terms of the numberofdivisors 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

Cf. A000005.
Sequence in context: A265018 A238792 A158745 * A265145 A103310 A046146
Adjacent sequences: A175105 A175106 A175107 * A175109 A175110 A175111


KEYWORD

nonn


AUTHOR

Leroy Quet, Feb 12 2010


EXTENSIONS

More terms from R. J. Mathar and Ray Chandler, Mar 05 2010


STATUS

approved



