190629

Ruby

sigma_{n-1}(n)

紛らわしいものを出力してみた。 

def s(n)
  s = 0
  (1..n).each{|i| s += i ** (i - 1) if n % i == 0}
  s
end

def t(n)
  s = 0
  (1..n).each{|i| s += i ** (n - 1) if n % i == 0}
  s
end

def u(n)
  s = 0
  (1..n).each{|i| s += n ** (i - 1) if n % i == 0}
  s
end

n = 20
# A262843
p (1..n).map{|i| s(i)}
# A082245
p (1..n).map{|i| t(i)}
# A308814
p (1..n).map{|i| u(i)}

出力結果
[1, 3, 10, 67, 626, 7788, 117650, 2097219, 43046731, 1000000628, 25937424602, 743008378540, 23298085122482, 793714773371796, 29192926025391260, 1152921504608944195, 48661191875666868482, 2185911559738739586477, 104127350297911241532842, 5242880000000001000000692]
[1, 3, 10, 73, 626, 8052, 117650, 2113665, 43053283, 1001953638, 25937424602, 743375541244, 23298085122482, 793811662272744, 29192932133689220, 1152956690052710401, 48661191875666868482, 2185928253847184914509, 104127350297911241532842, 5242890000019348364759358]
[1, 3, 10, 69, 626, 7819, 117650, 2097673, 43046803, 1000010011, 25937424602, 743008621405, 23298085122482, 793714780783695, 29192926025441476, 1152921504875286545, 48661191875666868482, 2185911559749718382455, 104127350297911241532842, 5242880000000512000168021]