Python-сообщество

 ni = {}
def partition(number):
    global ni
    answer = {(number,), }
    for x in range(1, number):
        for y in partition(number - x):
            answer.add(tuple(sorted((x, ) + y)))
    ni[number] = answer
    return answer
print('К-во разделов числа:')
for r in sorted(partition(5))[::-1]:
    print('\t' + ' + '.join(str(i) for i in r))