OFFSET
0,6
LINKS
FORMULA
a(n) = [x^n] Product_{d(k) = d(n)} 1/(1 - x^k).
EXAMPLE
a(27) = 3 because we have [27], [21, 6] and [15, 6, 6], where 27, 21, 15 and 6 are numbers with 4 divisors.
MAPLE
with(numtheory):
a:= proc(m) option remember; local k, b; k, b:= tau(m),
proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1)+`if`(tau(i)=k, b(n-i, min(i, n-i)), 0)))
end: b(m$2)
end:
seq(a(n), n=0..100); # Alois P. Heinz, Mar 17 2018
MATHEMATICA
Table[SeriesCoefficient[Product[1/(1 - Boole[DivisorSigma[0, k] == DivisorSigma[0, n]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 80}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 17 2018
STATUS
approved