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

1,1

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Intersection of A013929 and A005100.

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

Sequence in context: A175031 A052054 A046447 * A080062 A249125 A377819

Adjacent sequences: A087241 A087242 A087243 * A087245 A087246 A087247

Keyword

nonn

Author

Labos Elemer, Sep 05 2003

Status

approved