A075308 - OEIS

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..28.

FORMULA

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

EXAMPLE

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).

PROG

(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

CROSSREFS

Cf. A001597, A070428.

Sequence in context: A280118 A143555 A025234 * A300461 A280085 A322784

Adjacent sequences: A075305 A075306 A075307 * A075309 A075310 A075311

KEYWORD

nonn,base,easy

AUTHOR

Zak Seidov, Oct 11 2002

EXTENSIONS

More terms from Jinyuan Wang, Mar 02 2020

STATUS

approved