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

2520, 5040, 7560, 10080, 10800, 12600, 15120, 20160, 21600, 22680, 23760, 25200, 27720, 30240, 32400, 35280, 37800, 43200, 45360, 47520, 50400, 52920, 55440, 60480, 64800, 65520, 70560, 71280, 75600, 79200, 83160, 86400, 88200, 90720, 95040, 98280, 100800, 105840

Offset: 1

Author

Amiram Eldar, Jul 01 2025

Keywords

• nonn

Comments

Numbers k such that A050328(k) > k.

If k is a term then all the smaller numbers with the same prime signature (A118914) as k are also terms.

The least term that is not divisible by 5 is a(112) = 399168.

The least term that is not divisible by 3 is 144848704000.

The least odd term is A147516(43302) = 16639855392913235373515625.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A050328, A118914, A147516, A270308, A340155.

Programs

Mathematica

f[1] = 1; f[n_] := f[n] = DivisorSum[n, f[#] &, # < n && SquareFreeQ[n/#] &]; Select[Range[110000], f[#] > # &]

PARI

f(n) = if(n == 1, 1, sumdiv(n, d, if((d k;