cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A048108 #23 Jul 02 2025 16:01:57
%S A048108 8,16,24,27,32,36,40,48,54,56,64,72,80,81,88,96,100,104,108,112,120,
%T A048108 125,128,135,136,144,152,160,162,168,176,180,184,189,192,196,200,208,
%U A048108 216,224,225,232,240,243,248,250,252,256,264,270,272,280,288,296,297
%N A048108 Numbers with at least as many non-unitary divisors (A048105) as unitary divisors (A034444).
%C A048108 Numbers divisible by a prime cubed or two distinct primes squared. - _Charles R Greathouse IV_, Jun 07 2013
%C A048108 Equals A013929 \ A060687. The asymptotic density of this sequence is 1 - A059956 - A271971 = 0.1913171761... - _Amiram Eldar_, Nov 07 2020
%H A048108 Michael De Vlieger, <a href="/A048108/b048108.txt">Table of n, a(n) for n = 1..10000</a>
%p A048108 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 A048108 Select[Range[300], Function[n, # <= DivisorSigma[0, n] - # &@ DivisorSum[n, 1 &, CoprimeQ[#, n/#] &]]] (* or *)
%t A048108 Select[Range[300], Or[Count[#, p_ /; Last@ p >= 2] >= 2, Count[#, p_ /; Last@ p >= 3] == 1] &@ FactorInteger@ # &] (* _Michael De Vlieger_, Aug 01 2017 *)
%o A048108 (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 A048108 (PARI) is(n)=factorback(factor(n)[,2]) > 2 \\ _Charles R Greathouse IV_, Aug 25 2016
%Y A048108 Complement of A048107.
%Y A048108 Subsequence of A013929.
%Y A048108 Cf. A059956, A060687, A271971.
%K A048108 nonn
%O A048108 1,1
%A A048108 _N. J. A. Sloane_, _Labos Elemer_
%E A048108 More terms from _James Sellers_, Jun 20 2000