A075308 Number of n-digit perfect powers.

4, 8, 28, 84, 242, 744, 2284, 7096, 22179, 69561, 218759, 689206, 2173942, 6862783, 21676671, 68493153, 216477260, 684309327, 2163434093, 6840212693, 21628140126, 68388775913, 216252650605, 683825838922, 2162393136881, 6837971108286, 21623312527390, 68378377967873

Offset: 1

Author

Zak Seidov, Oct 11 2002

Keywords

• nonn
• base
• easy

Examples

			a(2) = 8 because there are eight 2-digit perfect powers: 16, 25, 27, 32, 36, 49, 64, 81.
a(3) = 28 = A070428(3) - A070428(2) = 41 - 13 (in A070428 offset is 0).
		

Crossrefs

Cf. A001597, A070428.

Programs

Python

from sympy import mobius, integer_nthroot
def A075308(n): return int(sum(mobius(x)*(integer_nthroot(10**(n-1),x)[0]-integer_nthroot(10**n,x)[0]) for x in range(2,((10**(n-1)).bit_length())))-sum(mobius(x)*(integer_nthroot(10**n,x)[0]-1) for x in range((10**(n-1)).bit_length(),(10**n).bit_length()))) if n>2 else n<<2 # Chai Wah Wu, Aug 13 2024

Formula

a(n) = A070428(n) - A070428(n-1) for n >= 3.

Extensions

More terms from Jinyuan Wang, Mar 02 2020