A248662 - OEIS

%I #26 Jun 22 2019 09:21:06

%S 1,120,144,180,216,240,252,288,300,336,360,420,432,480,504,540,576,

%T 600,630,648,660,672,720,756,792,810,840,864,900,960,1008,1050,1080,

%U 1120,1152,1176,1200,1260,1296,1320,1344,1350,1400,1440,1500,1512,1560

%N Numbers with the property: tau(n) > sopfr(n), or A000005(n) > A001414(n).

%C The number of divisors exceeds the sum of its prime factors, with repetition.

%C These are a subset of the abundant numbers = A005101.

%C The numbers where tau(n) = sopfr(n) are given by A078511.

%H Amiram Eldar, <a href="/A248662/b248662.txt">Table of n, a(n) for n = 1..10000</a>

%t ResultList = {1}; Do[

%t If[ (DivisorSigma[0, k] > Total[Times @@@ FactorInteger[k]]),

%t   AppendTo[ResultList, k]], {k, 2, 10000}]; ResultList

%o (PARI) isok(n) = my(f=factor(n)); sum(i=1,#f~,f[i,1]*f[i,2]) < numdiv(n); \\ _Michel Marcus_, Jun 22 2019

%Y Cf. A000005, A001414, A005101, A078511.

%K nonn

%O 1,2

%A _Richard R. Forberg_, Jan 15 2015

%E a(1) = 1 inserted by _Amiram Eldar_, Jun 22 2019