A388005 Sum of numbers <= 10^n which are not squarefree.

0, 21, 2083, 197424, 19584966, 1960338801, 196039437090, 19603447688113, 1960366145177114, 196036432880367943, 19603645661960386378, 1960364483871760080221, 196036448646623267072614, 19603644909860845684997031, 1960364490676476982289592054

Offset

0,2

Comments

Asymptotically ~ 0.19603645...*(10^n)^2 = (1/2-3/Pi^2)*(10^n)^2.

Links

Henri Lifchitz, Table of n, a(n) for n = 0..24 (terms 21..22 from Chai Wah Wu), Jan 10 2026

Formula

a(n) = (10^n)*(10^n+1)/2 - A387980(n).

Example

The first not squarefree numbers are: 4, 8, 9, 12, 16, ... So, a(1) = 4+8+9 = 21.

Mathematica

SumNotSquarefree[n_Integer?Positive] := Total@Select[Range[n], ! SquareFreeQ[#] &];
Table[SumNotSquarefree[10^n], {n, 0, 6}]

Prog

(Python)
from math import comb, isqrt
from sympy import mobius
def A388005(n): return -sum(mobius(k)*(s:=k**2)*comb(10**n//s+1, 2) for k in range(2, isqrt(10**n)+1)) # Chai Wah Wu, Oct 20 2025

Crossrefs

Cf. A013929, A037156, A063035, A387980.

Sequence in context: A265175 A300577 A304643 * A153848 A221771 A007593

Adjacent sequences: A388002 A388003 A388004 * A388006 A388007 A388008

Keyword

nonn

Author

Henri Lifchitz, Oct 14 2025

Status

approved