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

1,2

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 *)

Prog

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

Crossrefs

Cf. A006446, A079631.

Sequence in context: A050292 A181627 A071521 * A225553 A039733 A179510

Adjacent sequences: A204327 A204328 A204329 * A204331 A204332 A204333

Keyword

nonn

Author

Benoit Cloitre, Jan 14 2012

Extensions

Corrected by Geoffrey Critzer, May 25 2013

Status

approved