A289367
以下は、A289367 の出力と、288 で割り切れることの確認のためのコードです。
require 'prime'
# m次以下を取り出す
def mul(f_ary, b_ary, m)
s1, s2 = f_ary.size, b_ary.size
ary = Array.new(s1 + s2 - 1, 0)
(0..s1 - 1).each{|i|
(0..s2 - 1).each{|j|
ary[i + j] += f_ary[i] * b_ary[j]
}
}
ary[0..m]
end
def power0(a, n)
return 1 if n == 0
k = power0(a, n >> 1)
k *= k
return k if n & 1 == 0
return k * a
end
# x > 0
def sigma(x, i)
sum = 1
pq = i.prime_division
pq.each{|a, n| sum *= (power0(a, (n + 1) * x) - 1) / (power0(a, x) - 1)}
sum
end
def bernoulli(n)
ary = []
a = []
(0..n).each{|i|
a << 1r / (i + 1)
i.downto(1){|j| a[j - 1] = j * (a[j - 1] - a[j])}
ary << a[0] # Bn = a[0]
}
ary
end
def I(ary, n)
a = [1]
i = 0
while i < n
a << -(0..i).inject(0){|s, j| s + ary[1 + i - j] * a[j]}
i += 1
end
a
end
def E_2k(k, n)
a = (-4 * k / bernoulli(2 * k)[-1])
b = a.denominator
c = a.numerator
[b] + (1..n).map{|i| c * sigma(2 * k - 1, i)}
end
def A008683(n)
ary = n.prime_division
return (-1) ** (ary.size % 2) if ary.all?{|i| i[1] == 1}
0
end
def A(k, n)
a = mul(I(E_2k(k, n), n), E_2k(k + 1, n), n)
m_ary = [0] + (1..n).map{|i| A008683(i)}
ary = []
(1..n).each{|i|
s = 0
(1..i).each{|j|
s += m_ary[i / j] * a[j] if i % j == 0
}
ary << s / i
}
ary
end
def A289367(n)
ary3 = [0] + A(3, n)
ary2 = [0] + A(2, n)
(1..n).map{|i| (ary3[i] - ary2[i]) / 288}
end
def B(n)
ary3 = [0] + A(3, n)
ary2 = [0] + A(2, n)
(1..n).map{|i| (ary3[i] - ary2[i]) % 288}
end
p A289367(50)
p B(5000)
出力結果
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