How do I take in user input in discord.py

I'll start with answering your question, then I'll clarify on a better way to create a purge command. To answer your question, there is no need to make an input() statement. Rather, this is how you make an input prompt with a Discord bot:

@client.event
async def on_message(message):
    if message.author == client.user:
        return
    if message.content.startswith('p!purge'):
        await message.channel.send('How many messages do you want to purge?')

        while True:
            numberoftimes = client.wait_for('message')  # This means, the client is waiting for a message
            if numberoftimes.author == message.author:  # Make sure that the person responding is the person who did the command
                limit = int(numberoftimes.content)  # If its a string, it will be treated as a word. You want to purge a "number" of messages
        await message.channel.purge(limit=limit+1)

That's how you would purge messages in a channel. But, the way you are creating this command can be made simpler. You can use the command decorator, which is the "standard" way of doing things:

import discord
from discord.ext import commands

client = commands.Bot(command_prefix='p!')

@client.command()
@commands.has_permissions(manage_messages=True)
async def purge(ctx, limit):
    limit = int(limit)
    await ctx.channel.purge(limit=limit + 1)