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

Robert Israel, Table of n, a(n) for n = 1..10000

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.

Maple

f:= proc(n) nops(select(t -> n mod t = 0 or numtheory:-issqrfree(t), [$1..n])) end proc:
map(f, [$1..100]); # Robert Israel, Dec 09 2024

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