A087244 Nonsquarefree deficient numbers.

4, 8, 9, 16, 25, 27, 32, 44, 45, 49, 50, 52, 63, 64, 68, 75, 76, 81, 92, 98, 99, 116, 117, 121, 124, 125, 128, 135, 136, 147, 148, 152, 153, 164, 169, 171, 172, 175, 184, 188, 189, 207, 212, 225, 232, 236, 242, 243, 244, 245, 248, 250, 256, 261, 268, 275, 279

Offset: 1

Author

Labos Elemer, Sep 05 2003

Keywords

• nonn

Comments

The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 3, 21, 197, 1982, 19913, 199871, 1995546, 19967891, 199695593, 1996670090, ... . Apparently, the asymptotic density of this sequence exists and equals 0.1996... . - Amiram Eldar, Dec 29 2024

Examples

			m = 45 - 3*3*5 and sigma(45) = 78 < 2m = 90.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A013929 and A005100.

Cf. A087245, A087246, A087247, A008683, A000203, A005117, A005101.

Programs

Mathematica

Select[Range@ 280, And[! SquareFreeQ@ #, DivisorSigma[1, #] < 2 #] &] (* Michael De Vlieger, Mar 25 2017 *)

PARI

isok(n) = !issquarefree(n) && (sigma(n) < 2*n); \\ Michel Marcus, Dec 18 2013

Python

from sympy import divisor_sigma
from sympy.ntheory.factor_ import core
print([n for n in range(1,301) if core(n) != n and divisor_sigma(n)<2*n]) # Indranil Ghosh, Mar 26 2017