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A385511 Numbers that are less than the number of their ordered factorizations into squarefree numbers greater than 1.

%I A385511 #7 Jul 01 2025 10:14:12
%S A385511 2520,5040,7560,10080,10800,12600,15120,20160,21600,22680,23760,25200,
%T A385511 27720,30240,32400,35280,37800,43200,45360,47520,50400,52920,55440,
%U A385511 60480,64800,65520,70560,71280,75600,79200,83160,86400,88200,90720,95040,98280,100800,105840
%N A385511 Numbers that are less than the number of their ordered factorizations into squarefree numbers greater than 1.
%C A385511 Numbers k such that A050328(k) > k.
%C A385511 If k is a term then all the smaller numbers with the same prime signature (A118914) as k are also terms.
%C A385511 The least term that is not divisible by 5 is a(112) = 399168.
%C A385511 The least term that is not divisible by 3 is 144848704000.
%C A385511 The least odd term is A147516(43302) = 16639855392913235373515625.
%H A385511 Amiram Eldar, <a href="/A385511/b385511.txt">Table of n, a(n) for n = 1..10000</a>
%t A385511 f[1] = 1; f[n_] := f[n] = DivisorSum[n, f[#] &, # < n && SquareFreeQ[n/#] &]; Select[Range[110000], f[#] > # &]
%o A385511 (PARI) f(n) = if(n == 1, 1, sumdiv(n, d, if((d<n && issquarefree(n/d)), f(d))));
%o A385511 isok(k) = f(k) > k;
%Y A385511 Cf. A005117, A050328, A118914, A147516, A270308, A340155.
%K A385511 nonn
%O A385511 1,1
%A A385511 _Amiram Eldar_, Jul 01 2025