Find-the-number-of-numbers-10-8-which-are-neither-perfect-squares-nor-perfect-cubes-nor-perfect-fifth-powers-

Question Number 18949 by Tinkutara last updated on 01/Aug/17

Find the number of numbers ⩽ 10^{8}

which are neither perfect squares, nor

perfect cubes, nor perfect fifth powers .

Commented by prakash jain last updated on 03/Aug/17

i retyped the answer .

Answered by prakash jain last updated on 03/Aug/17

no of perfect squares = 10^{4}

no of perfect cubes = 464

no of perfect power 5 = 39

no of perfect power 6 = 21

no of perfect power 15 = 3

no of perfect power 10 = 6

no of perfect power 30 = 1

number of perfect squares

cubes and power 5

n = 10000 + 464 + 39 - 21 - 3 - 6 + 1

requited answer = 10^{8} - n

Commented by Tinkutara last updated on 03/Aug/17

Thank you very much Sir!