cp's OEIS Frontend

A048111 Number of unitary divisors of n (A034444) < number of non-unitary divisors of n (A048105).

%I A048111 #35 Sep 25 2022 04:26:11
%S A048111 16,32,36,48,64,72,80,81,96,100,108,112,128,144,160,162,176,180,192,
%T A048111 196,200,208,216,224,225,240,243,252,256,272,288,300,304,320,324,336,
%U A048111 352,360,368,384,392,396,400,405,416,432,441,448,450,464,468,480,484
%N A048111 Number of unitary divisors of n (A034444) < number of non-unitary divisors of n (A048105).
%C A048111 Numbers n that are expressible as a product of 2 "nonsquarefree" numbers (i.e., there are 2 integers x,y in A001694 such that n = xy). - _Benoit Cloitre_, Jan 01 2003
%C A048111 Also numbers having more than one square divisor > 1: A046951(a(n)) > 2. - _Reinhard Zumkeller_, Apr 08 2003
%C A048111 The asymptotic density of this sequence is 1 - (6/Pi^2)*(1 + Sum_{n>=1} 1/prime(n)^2) = 1 - A059956 * (1 + A085548) = 0.1171394347594477824... . - _Amiram Eldar_, Sep 25 2022
%H A048111 Amiram Eldar, <a href="/A048111/b048111.txt">Table of n, a(n) for n = 1..10000</a>
%F A048111 A000005(a(n)) > 2^(1 + A001221(a(n))).
%e A048111 36 is in the sequence since the number of its unitary divisors, {1, 4, 9, 36} is 4 which is smaller than 5, the number of its non-unitary divisors, {2, 3, 6, 12, 18}.
%t A048111 Select[Range[484], DivisorSigma[0, #] > 2^(PrimeNu[#]+1) &] (* _Amiram Eldar_, Jun 11 2019 *)
%o A048111 (PARI) is(n)=my(f=factor(n)[,2],t); for(i=1,#f,if(f[i]>1, if(t||f[i]>3, return(1), t=1))); 0 \\ _Charles R Greathouse IV_, Sep 17 2015
%Y A048111 Cf. A000005, A001221, A034444, A048105, A048109, A082293, A013929, A082294, A082295.
%Y A048111 Cf. A085548, A059956.
%K A048111 nonn
%O A048111 1,1
%A A048111 _Labos Elemer_