A069291 Number of square divisors of n <= sqrt(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2

Offset: 1

Author

Reinhard Zumkeller, Mar 14 2002

Keywords

• nonn

Comments

Terms 1, 2, 3, ... occurs for the first time at 1, 16, 108, 288, 1296, 3600, 10368, 14400, ... - Antti Karttunen, Nov 20 2017

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000188, A035316, A046951, A069290, A069292, A069293.

Programs

Mathematica

Table[DivisorSum[n, 1 &, And[IntegerQ@ Sqrt@ #, # <= Sqrt@ n] &], {n, 120}] (* Michael De Vlieger, Nov 20 2017 *)

PARI

A069291(n) = sumdiv(n, d, (issquare(d)&&((d^2)<=n))); \\ Antti Karttunen, Nov 20 2017

Formula

G.f.: Sum_{k>=1} x^(k^4) / (1 - x^(k^2)). - Ilya Gutkovskiy, Apr 04 2020

Extensions

More terms from Antti Karttunen, Nov 20 2017