A170925 G.f.: eta(q)*eta(q^2)*eta(q^4)*eta(q^8)*eta(q^16)*eta(q^32)*..., where eta(q) = Product((1-q^m), m=1..oo).

1, -1, -2, 1, -1, 3, 3, -1, -2, -2, 4, -4, -1, -3, -3, 2, 1, 9, -1, 6, 7, -8, -10, 1, -1, 0, -2, 0, 2, -1, 4, -4, -1, -5, 14, -15, -7, 9, 11, 7, 0, 3, -14, 17, -7, 18, 4, -6, -7, -25, -12, -5, -13, -3, 9, -14, 25, 10, -2, 8, 17, 1, 2, 13, 4, 0, -4, 7, 13, -27, -42, 11, 5, 5, 10, -24, 3, -21, -4, 0, -32, 27, 29, -1, -4, 43, 26, -7, -41, -9, 27, -11

Offset: 0

Author

N. J. A. Sloane and Gary W. Adamson, Feb 18 2010

Keywords

• sign

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

Crossrefs

Cf. A010815, A083650, A030189, A160832, A143374, A194087.

Programs

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 *)

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