A351520 Number of numbers <= n that are either squarefree, a divisor of n, or both.

1, 2, 3, 4, 4, 5, 6, 8, 7, 7, 8, 10, 9, 10, 11, 14, 12, 14, 13, 15, 14, 15, 16, 20, 17, 17, 19, 19, 18, 19, 20, 24, 21, 22, 23, 28, 24, 25, 26, 30, 27, 28, 29, 31, 31, 30, 31, 37, 32, 33, 32, 34, 33, 37, 34, 38, 35, 36, 37, 41, 38, 39, 41, 44, 40, 41, 42, 44, 43, 44, 45, 53, 46, 47, 49

Offset

1,2

Links

Table of n, a(n) for n=1..75.

Formula

a(n) = tau(n) + Sum_{k=1..n} mu(k)^2 - Sum_{d|n} mu(d)^2.

a(n) = A000005(n) + A013928(n+1) - A034444(n).

Example

a(10) = 7; There are 7 numbers less than or equal to 10 that are either squarefree, a divisor of 10, or both. The numbers are 1,2,3,5,6,7,10.

Mathematica

Module[{nn=80, sf}, sf=Select[Range[nn], SquareFreeQ[#]&]; Table[Length[Union[Select[sf, #<= n&], Divisors[n]]], {n, nn}]] (* Harvey P. Dale, Jul 03 2023 *)

Crossrefs

Cf. A000005 (tau), A013928, A034444.

Sequence in context: A356860 A017865 A317143 * A065328 A049877 A029063

Adjacent sequences: A351517 A351518 A351519 * A351521 A351522 A351523

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 12 2022

Status

approved