# The greatest length of a block of consecutive strange numbers is? A integer(>$0$)is said to be strange if all powers are odd in prime factorisation.

A positive integer is said to be strange if all powers are odd in their prime factorisation. For instance, $$22,23,24$$ form a block of consecutive strange numbers because $$22=2^1\times11^1,23=23^1,24=2^3\times3^1$$. What is the greatest length of a block of consecutive strange numbers?

I tried all the numbers till 50 and obtained two series with $$7$$ terms which is the answer. The consecutive numbers are:- $$S_1=29,30,31,32,33,34,35\\S_2=37,38,39,40,41,42,43$$How can we make sure that we cannot find any series with more than $$7$$ terms?

• If x is 4 mod 8, then x is not strange.
– Eric
May 29 at 3:03
• Do you mean that all the exponents in the prime factorizations are odd ? May 30 at 9:33
• @Eric Why not formulate this as an answer ? I would galdly upvote it. May 30 at 9:35