A048108 Numbers with at least as many non-unitary divisors (A048105) as unitary divisors (A034444).

8, 16, 24, 27, 32, 36, 40, 48, 54, 56, 64, 72, 80, 81, 88, 96, 100, 104, 108, 112, 120, 125, 128, 135, 136, 144, 152, 160, 162, 168, 176, 180, 184, 189, 192, 196, 200, 208, 216, 224, 225, 232, 240, 243, 248, 250, 252, 256, 264, 270, 272, 280, 288, 296, 297

Offset: 1

Author

N. J. A. Sloane, Labos Elemer

Keywords

• nonn

Comments

Numbers divisible by a prime cubed or two distinct primes squared. - Charles R Greathouse IV, Jun 07 2013

Equals A013929 \ A060687. The asymptotic density of this sequence is 1 - A059956 - A271971 = 0.1913171761... - Amiram Eldar, Nov 07 2020

Links

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

Crossrefs

Complement of A048107.

Subsequence of A013929.

Cf. A059956, A060687, A271971.

Programs

Maple

with(numtheory): for n from 1 to 800 do if 2^nops(ifactors(n)[2])<=tau(n)-2^nops(ifactors(n)[2]) then printf(`%d,`,n) fi; od:

Mathematica

Select[Range[300], Function[n, # <= DivisorSigma[0, n] - # &@ DivisorSum[n, 1 &, CoprimeQ[#, n/#] &]]] (* or *)
Select[Range[300], Or[Count[#, p_ /; Last@ p >= 2] >= 2, Count[#, p_ /; Last@ p >= 3] == 1] &@ FactorInteger@ # &] (* Michael De Vlieger, Aug 01 2017 *)

PARI

is(n)=my(f=vecsort(factor(n)[,2],,4));#f && (f[1]>2 || (#f>1 && f[2]>1)) \\ Charles R Greathouse IV, Jun 07 2013

PARI

is(n)=factorback(factor(n)[,2]) > 2 \\ Charles R Greathouse IV, Aug 25 2016

Extensions

More terms from James Sellers, Jun 20 2000