OFFSET
0,3
COMMENTS
eta(q) = A(q)/A(q^2), where A(q) is the g.f. for this sequence (cf. A010815).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[QPochhammer[x^(2^k)], {k, 0, Log[nmax]/Log[2]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 23 2019 *)
PROG
(Ruby)
def s(k, n)
s = 0
(1..n).each{|i| s += i if n % i == 0 && i % k == 0}
s
end
def A(ary, n)
a_ary = [1]
a = [0] + (1..n).map{|i| ary.inject(0){|s, j| s + j[1] * s(j[0], i)}}
(1..n).each{|i| a_ary << (1..i).inject(0){|s, j| s - a[j] * a_ary[-j]} / i}
a_ary
end
def A170925(n)
A((0..Math.log(n, 2)).map{|i| [2 ** i, 1]}, n)
end
p A170925(100) # Seiichi Manyama, Sep 23 2019
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane and Gary W. Adamson, Feb 18 2010
STATUS
approved