A344181 Numbers such that repeated division by their largest factorial divisor (as long as such a divisor larger than one exists) eventually yields 1.

1, 2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64, 96, 120, 128, 144, 192, 240, 256, 288, 384, 480, 512, 576, 720, 768, 864, 960, 1024, 1152, 1440, 1536, 1920, 2048, 2304, 2880, 3072, 3456, 3840, 4096, 4320, 4608, 5040, 5760, 6144, 6912, 7680, 8192, 8640, 9216, 10080

Offset

1,2

Comments

Numbers whose closure under map x -> A076934(x) contains 1.

Largest factorial divisor of n is A000142(A055874(n)).

These numbers could be called "greedy Jordan-Polya numbers", as their presence in A001013 can be determined by a simple greedy algorithm.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Index entries for sequences related to factorial numbers

Example

12 = 2^2 * 3 is present, as the largest factorial that divides 12 is A000142(3) = 6, and then 12/6 = 2 is also divisible by a factorial, and then 2/A000142(2) = 1.

Mathematica

fctdiv[n_] := Module[{m = 1, k = 1}, While[Divisible[n, m], k++; m *= k]; m /= k; n/m]; Select[Range[10^4], FixedPoint[fctdiv, #] == 1 &] (* Amiram Eldar, May 22 2021 *)

Crossrefs

Cf. A000142, A055874, A076934.

Positions of ones in A093411.

Subsequence of A001013. A344179 gives the terms not present here.

Cf. also A025487 (analogous sequence for primorials).

Sequence in context: A001013 A115746 A025610 * A242101 A131117 A332290

Adjacent sequences: A344178 A344179 A344180 * A344182 A344183 A344184

Keyword

nonn

Author

Antti Karttunen, May 18 2021

Status

approved