A095686 - OEIS

A095686

Half the number of divisors of nonsquares (A000037).

1, 1, 1, 2, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 1, 4, 1, 3, 2, 2, 2, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 5, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 6, 1, 2, 3, 2, 4, 1, 3, 2, 4, 1, 6, 1, 2, 3, 3, 2, 4, 1, 5, 2, 1, 6, 2, 2, 2, 4, 1, 6, 2, 3, 2, 2, 2, 6, 1, 3, 3, 1, 4, 1, 4, 4, 2, 1, 6, 1, 4, 2, 5, 1, 4, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

The first occurrence of n in the sequence corresponds to the nonsquare = A003680(n) = A005179(2n).

Also number of unordered divisor pairs (d,n/d) for n=A000037. - Lekraj Beedassy, Jul 30 2004

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n)=A000005(A000037(n))/2.

MATHEMATICA

m=11; DivisorSigma[0, Complement[Range[m^2], Range[m]^2]]/2 (* Amiram Eldar, Nov 05 2019 *)

PROG

(PARI) lista(nn) = {for (i = 1, nn, if (! issquare(i), print1(numdiv(i)/2, ", ")); ); } \\ Michel Marcus, Jul 27 2013

(Python)

from math import isqrt

from sympy import divisor_count

def A095686(n): return divisor_count(n+(k:=isqrt(n))+int(n>k*(k+1)))>>1 # Chai Wah Wu, Jun 05 2025

CROSSREFS

Sequence in context: A224362 A350560 A050362 * A105258 A329173 A366493

Adjacent sequences: A095683 A095684 A095685 * A095687 A095688 A095689

KEYWORD

nonn

AUTHOR

Lekraj Beedassy, Jul 05 2004

EXTENSIONS

Corrected and extended by Ray Chandler, Jul 09 2004

STATUS

approved