A285881 Number of even squarefree numbers <= n.

0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18

Offset

1,6

Links

Table of n, a(n) for n=1..85.

Eric Weisstein's World of Mathematics, Squarefree

Formula

G.f.: Sum_{k>=1} x^A039956(k)/(1 - x).

a(n) ~ 2*n/Pi^2.

From Ridouane Oudra, Apr 17 2026: (Start)

a(n) = Sum_{k=1..floor(n/2)} A323239(k).

a(n) = Sum_{k=1..floor(n/2)} A359548(k)*floor(n/(2*k)).

a(n) = Sum_{k=1..floor(sqrt(n/2))} A087003(k)*round(n/(4*k^2)).

a(n) = A013928(n+1) - A285879(n).

a(n) = A285879(floor(n/2)). (End)

Mathematica

Table[Sum[Boole[EvenQ[k] && SquareFreeQ[k]], {k, 1, n}], {n, 85}]
nmax = 85; Rest[CoefficientList[Series[Sum[Boole[EvenQ[k] && MoebiusMu[k]^2 == 1] x^k/(1 - x), {k, 1, nmax}], {x, 0, nmax}], x]]

Prog

(Python)
from sympy.ntheory.factor_ import core
def a(n): return sum([1 for k in range(1, n + 1) if k%2==0 and core(k)==k]) # Indranil Ghosh, Apr 28 2017

Crossrefs

Cf. A005117, A008683, A013928, A039956, A285879, A323239, A359548, A087003,

Sequence in context: A169990 A055679 A056172 * A091373 A385652 A197637

Adjacent sequences: A285878 A285879 A285880 * A285882 A285883 A285884

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 27 2017

Status

approved