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

1,1

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.

Links

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

Index entries for sequences related to factorial numbers

Example

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.

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 *)

Prog

(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]<n, -(1/0), ((1!=A093411(n))&&vecsearch(v001013, n)));
for(n=1, search_up_to, if(isA344179(n), print1(n, ", ")));

Crossrefs

Setwise difference of A001013 and A344181.

Cf. A000142, A055874, A076934, A093411.

Sequence in context: A204492 A204485 A358514 * A050498 A077535 A339994

Adjacent sequences: A344176 A344177 A344178 * A344180 A344181 A344182

Keyword

nonn

Author

Antti Karttunen, May 18 2021

Status

approved