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A270308
Numbers which are less than the number of their ordered factorizations.
3
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
1,1
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
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..100 from Paolo P. Lava)
FORMULA
Solution of the inequation n < A002033(n-1) = A074206(n).
EXAMPLE
The ordered partitions of 72 are 76, of 96 are 112, of 120 are 132, etc.
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<a[j] then print(j); fi; od; end: P(10^5);
MATHEMATICA
f[1] = 1; f[n_] := DivisorSum[n, f[#] &, # < n &]; Select[Range[2400], f[#] > # &] (* Amiram Eldar, Apr 11 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Mar 15 2016
STATUS
approved