A344179 Jordan-Polya numbers (A001013) not in A344181.

72, 216, 432, 1296, 1728, 2592, 5184, 7776, 10368, 14400, 15552, 28800, 31104, 41472, 46656, 51840, 57600, 62208, 93312, 115200, 120960, 124416, 155520, 186624, 230400, 248832, 279936, 311040, 373248, 460800, 559872, 604800, 746496, 921600, 933120, 995328, 1088640, 1119744, 1209600, 1244160, 1492992, 1679616, 1728000

Offset: 1

Author

Antti Karttunen, May 18 2021

Keywords

• nonn

Comments

These are numbers that are products of factorial numbers (A000142), but whose presence in A001013 cannot be determined by a simple greedy algorithm that repeatedly divides the largest factorial divisor [= A055874(n)!] off, until only 1 remains.

Examples

			72 = 2*6*6 = 2! * 3! * 3! is present in A001013, and as it is not present in A344181 (because when it is divided by its largest factorial divisor 24, we get 72/24 = 3, an odd number that is not a factorial itself), it is therefore present in this sequence.
		

Links

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

Crossrefs

Setwise difference of A001013 and A344181.

Cf. A000142, A055874, A076934, A093411.

Programs

Mathematica

fct = Array[#! &, 10]; prev = {}; jp = fct; While[jp != prev, prev = jp; jp = Select[Union @@ Outer[Times, jp, fct], # <= fct[[-1]] &]]; fctdiv[n_] := Module[{m = 1, k = 1}, While[Divisible[n, m], k++; m *= k]; m /= k; n/m]; Select[jp, FixedPoint[fctdiv, #] != 1 &] (* Amiram Eldar, May 22 2021 *)

PARI

search_up_to = 2^22;
A076934(n) = for(k=2, oo , if(n%k, return(n), n /= k));
A093411(n) = if(!n,n, if(n%2, n, A093411(A076934(n))));
A001013list(lim, mx=lim)=if(lim<2, return([1])); my(v=[1], t=1); for(n=2, mx, t*=n; if(t>lim, break); v=concat(v, t*A001013list(lim\t, t))); Set(v) \\ From A001013
v001013 = A001013list(search_up_to);
A001013(n) = v001013[n];
isA344179(n) = if(v001013[#v001013]A093411(n))&&vecsearch(v001013,n)));
for(n=1,search_up_to,if(isA344179(n),print1(n,", ")));