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A351520
Number of numbers <= n that are either squarefree, a divisor of n, or both.
0
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Feb 12 2022
STATUS
approved