


def        snake_case_					(  snake_case=2_81_23					)  ->    Optional[int]:
       lowercase__:       Any        =       [1] * (limit + 1)

       for i in range(2      ,							int(limit**0.5					) + 1					):
              sum_divs[i * i] += i
              for k in range(i + 1      ,							limit // i + 1					):
                     sum_divs[k * i] += k + i

       lowercase__:       int        =       set()
       lowercase__:       int        =       0

       for n in range(1      ,							limit + 1					):
              if sum_divs[n] > n:
                     abundants.add(snake_case					)

              if not any((n - a in abundants) for a in abundants					):
                     res += n

       return res


if __name__ == "__main__":
 print(solution())








import math

import numpy as np
import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute




def        snake_case_					(  snake_case = 3					)  ->    qiskit.result.counts.Counts:
       if isinstance(snake_case      ,							snake_case					):
              raise TypeError('number of qubits must be a integer.'					)
       if number_of_qubits <= 0:
              raise ValueError('number of qubits must be > 0.'					)
       if math.floor(snake_case					) != number_of_qubits:
              raise ValueError('number of qubits must be exact integer.'					)
       if number_of_qubits > 10:
              raise ValueError('number of qubits too large to simulate(>10).'					)

       lowercase__:       str        =       QuantumRegister(snake_case      ,							'qr'					)
       lowercase__:       str        =       ClassicalRegister(snake_case      ,							'cr'					)

       lowercase__:       List[Any]        =       QuantumCircuit(snake_case      ,							snake_case					)

       lowercase__:       int        =       number_of_qubits

       for i in range(snake_case					):
              quantum_circuit.h(number_of_qubits - i - 1					)
              counter -= 1
              for j in range(snake_case					):
                     quantum_circuit.cp(np.pi / 2 ** (counter - j)      ,							snake_case      ,							snake_case					)

       for k in range(number_of_qubits // 2					):
              quantum_circuit.swap(snake_case      ,							number_of_qubits - k - 1					)

       # measure all the qubits
       quantum_circuit.measure(snake_case      ,							snake_case					)
       # simulate with 10000 shots
       lowercase__:       str        =       Aer.get_backend('qasm_simulator'					)
       lowercase__:       Union[str, Any]        =       execute(snake_case      ,							snake_case      ,							shots=1_00_00					)

       return job.result().get_counts(snake_case					)


if __name__ == "__main__":
 print(
     F'''Total count for quantum fourier transform state is: \
    {quantum_fourier_transform(3)}'''
 )


