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

Author

Antti Karttunen, May 18 2021

Keywords

• nonn

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.

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to factorial numbers

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).

Programs

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 *)