A270308 Numbers which are less than the number of their ordered factorizations.

72, 96, 120, 144, 192, 216, 240, 288, 336, 360, 384, 432, 480, 504, 540, 576, 600, 648, 672, 720, 768, 840, 864, 960, 1008, 1080, 1152, 1200, 1260, 1296, 1344, 1440, 1512, 1536, 1584, 1620, 1680, 1728, 1800, 1872, 1920, 1944, 2016, 2112, 2160, 2240, 2304, 2400

Offset: 1

Author

Paolo P. Lava, Mar 15 2016

Keywords

• nonn
• easy

Comments

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

The least odd term of this sequence is 51288546684375. - Amiram Eldar, Apr 11 2020

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..100 from Paolo P. Lava)

Crossrefs

Cf. A002033, A074206, A163272.

Programs

Maple

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;
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;
if j
				

Mathematica

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

Formula

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