Problem A Python

Integer Properties

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en

is

Write a program that does the following:

First, repeatedly checks whether an integer has

positive divisors or more. A number

is said to be a divisor of

if there is no remainder after dividing

by

$.$ The repetition should stop as soon as q or Q is entered.

Second, reads the integer

from the keyboard. Finds and prints:

all positive two digit integers up to and including

whose digit sum squared is equal to the integer in question;

and all positive three digit integers up to and including

whose digit sum cubed is equal to the integer in question.

The digit sum of an integer

is found by taking each digit of

and adding them all together.

Input

First, the input for part one will be provided: Zero or more integers will appear in the input, each on its own line, followed by a line containing only a q or a Q$,$ which indicates the repetition should stop.

Then, the input for part two follows: One line containing the integer

$.$

You may assume that each integer in the input will be between

and

$.$

Output

For each integer input in the first part, the program outputs yes if the integer has

or more positive divisors, otherwise it outputs no$.$

Then the program outputs the integers found in part two in ascending order, each on its own line.

The program must handle input and output in the correct order. In other words, it cannot read the next integer before producing the output for the previous one.