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

1,1

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

Mathematica

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

Prog

(PARI) f(n) = if(n == 1, 1, sumdiv(n, d, if((d<n && issquarefree(n/d)), f(d))));
isok(k) = f(k) > k;

Crossrefs

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

Sequence in context: A094515 A179700 A066531 * A258540 A159214 A224542

Adjacent sequences: A385508 A385509 A385510 * A385512 A385513 A385514

Keyword

nonn

Author

Amiram Eldar, Jul 01 2025

Status

approved