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

Offset: 1

Author

Benoit Cloitre, Jan 14 2012

Keywords

• nonn

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

• B. Cloitre, Some divisibility sequences

Crossrefs

Cf. A006446, A079631.

Programs

Mathematica

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

PARI

a(n)=sum(k=1,n,if(k%sqrtint(k),0,1));

Formula

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

Extensions

Corrected by Geoffrey Critzer, May 25 2013