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Odd and even divisors

Source: 2012-2013 SDML Middle School 1a Problem 12

August 24, 2016

Problem Statement

How many 22-digit integers have an equal number of odd and even positive divisors?
(A) 11(B) 12(C) 22(D) 23(E) 45\text{(A) }11\qquad\text{(B) }12\qquad\text{(C) }22\qquad\text{(D) }23\qquad\text{(E) }45