A204330 - OEIS

A204330

a(n) is the number of k satisfying 1 <= k <= n and such that floor(sqrt(k)) divides k.

1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 7, 8, 8, 8, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 21, 22, 22, 22, 22, 22, 22, 22

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OFFSET

1,2

COMMENTS

a(n) = floor(2*sqrt(n)) + floor(sqrt(n-1)) - 1 if n belongs to A135106 otherwise a(n) = floor(2*sqrt(n)) + floor(sqrt(n-1)) - 2.

LINKS

Table of n, a(n) for n=1..70.

B. Cloitre, Some divisibility sequences

FORMULA

a(n) = card{j>=1, A006446(j)<=n}.

MATHEMATICA

Accumulate[Boole[Table[IntegerQ[n/Floor[n^(1/2)]], {n, 1, 70}]]] (* Geoffrey Critzer, May 25 2013 *)