A048108 - OEIS

%I #22 Nov 07 2020 08:58:23

%S 8,16,24,27,32,36,40,48,54,56,64,72,80,81,88,96,100,104,108,112,120,

%T 125,128,135,136,144,152,160,162,168,176,180,184,189,192,196,200,208,

%U 216,224,225,232,240,243,248,250,252,256,264,270,272,280,288,296,297

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

%C Numbers divisible by a prime cubed or two distinct primes squared. - _Charles R Greathouse IV_, Jun 07 2013

%C Equals A013929 \ A060687. The asymptotic density of this sequence is 1 - A059956 - A271971 = 0.1913171761... - _Amiram Eldar_, Nov 07 2020

%H Michael De Vlieger, <a href="/A048108/b048108.txt">Table of n, a(n) for n = 1..10000</a>

%p 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:

%t Select[Range[300], Function[n, # <= DivisorSigma[0, n] - # &@ DivisorSum[n, 1 &, CoprimeQ[#, n/#] &]]] (* or *)

%t Select[Range[300], Or[Count[#, p_ /; Last@ p >= 2] >= 2, Count[#, p_ /; Last@ p >= 3] == 1] &@ FactorInteger@ # &] (* _Michael De Vlieger_, Aug 01 2017 *)

%o (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

%o (PARI) is(n)=factorback(factor(n)[,2]) > 2 \\ _Charles R Greathouse IV_, Aug 25 2016

%Y Complement of A048107.

%Y Subsequence of A013929.

%Y Cf. A059956, A060687, A271971.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, _Labos Elemer_

%E More terms from _James A. Sellers_, Jun 20 2000