A374812 10^n-th nonsquarefree number.

4, 27, 260, 2550, 25506, 255051, 2550519, 25505464, 255054546, 2550546152, 25505460948, 255054609189, 2550546096325, 25505460966984, 255054609673752, 2550546096737236, 25505460967313208, 255054609673067871, 2550546096730376472, 25505460967304302850, 255054609673042999696, 2550546096730430494608

Offset

0,1

Comments

a(n)/10^n converges to Pi^2/(Pi^2-6) = zeta(2)/(zeta(2)-1) as n -> oo. - Chai Wah Wu, Jul 21 2024

Links

Table of n, a(n) for n=0..21.

Chai Wah Wu, Algorithms for complementary sequences, arXiv:2409.05844 [math.NT], 2024.

Formula

a(n) = A013929(10^n).

Prog

(Python)
from functools import lru_cache
from math import isqrt
from sympy import mobius
def A374812(n):
    r = 10**n
    @lru_cache(maxsize=None)
    def g(x): return mobius(x)
    def f(x): return r+sum(g(k)*(x//k**2) for k in range(1, isqrt(x)+1))
    m, k = r, f(r)
    while m != k:
        m, k = k, f(k)
    return m

Crossrefs

Cf. A005117, A013661, A013929, A140809.

Sequence in context: A360032 A360833 A360835 * A302836 A301335 A362701

Adjacent sequences: A374809 A374810 A374811 * A374813 A374814 A374815

Keyword

nonn

Author

Chai Wah Wu, Jul 20 2024

Extensions

a(15) from Chai Wah Wu, Jul 21 2024

a(16)-a(21) from Chai Wah Wu, Aug 08 2024

Status

approved