A270308 - OEIS

%I #20 Apr 11 2020 06:12:15

%S 72,96,120,144,192,216,240,288,336,360,384,432,480,504,540,576,600,

%T 648,672,720,768,840,864,960,1008,1080,1152,1200,1260,1296,1344,1440,

%U 1512,1536,1584,1620,1680,1728,1800,1872,1920,1944,2016,2112,2160,2240,2304,2400

%N Numbers which are less than the number of their ordered factorizations.

%C Also numbers which are less than the number of their perfect factorizations or gozinta chains.

%C The least odd term of this sequence is 51288546684375. - _Amiram Eldar_, Apr 11 2020

%H Amiram Eldar, <a href="/A270308/b270308.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..100 from Paolo P. Lava)

%F Solution of the inequation n < A002033(n-1) = A074206(n).

%e The ordered partitions of 72 are 76, of 96 are 112, of 120 are 132, etc.

%p P:=proc(q) local a,j,k,m; a:= array(1..q); for k from 1 to q do a[k]:=0 od; a[1]:=1;

%p for j from 2 to q do for m from 1 to j-1 do if j mod m=0 then a[j]:= a[j]+a[m]; fi; od;

%p if j<a[j] then print(j); fi; od; end: P(10^5);

%t f[1] = 1; f[n_] := DivisorSum[n, f[#] &, # < n &]; Select[Range[2400], f[#] > # &] (* _Amiram Eldar_, Apr 11 2020 *)

%Y Cf. A002033, A074206, A163272.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Mar 15 2016