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Call an integer \(n\) oddly powerful if there exist positive integers \(a\) and \(b\), where \(b>1\)\(b\) is odd, and \(a^b = n\). How many oddly powerful integers are less than 2010?

 Jan 4, 2019
 #1
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I count 17 "oddly powerful integers":
(1, 8, 27, 32, 64, 125, 128, 216, 243, 343, 512, 512, 729, 1000, 1024, 1331, 1728)= 17 -"oddly powerful" integers!!.


1^3=1, 2^3 =8, 3^3=27, 2^5 =32, 4^3=64, 5^3 =125, 2^7=128, 6^3 =216, 3^5 =243, 7^3 =343, 2^9 =512, 8^3 =512, 9^3 =729, 10^3=1,000, 4^5 =1,024, 11^3 =1,331, 12^3 =1,728.

 Jan 4, 2019

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