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

%I A344179 #22 May 22 2021 04:28:43
%S A344179 72,216,432,1296,1728,2592,5184,7776,10368,14400,15552,28800,31104,
%T A344179 41472,46656,51840,57600,62208,93312,115200,120960,124416,155520,
%U A344179 186624,230400,248832,279936,311040,373248,460800,559872,604800,746496,921600,933120,995328,1088640,1119744,1209600,1244160,1492992,1679616,1728000
%N A344179 Jordan-Polya numbers (A001013) not in A344181.
%C A344179 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.
%H A344179 David A. Corneth, <a href="/A344179/b344179.txt">Table of n, a(n) for n = 1..10000</a>
%H A344179 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%e A344179 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.
%t A344179 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 *)
%o A344179 (PARI)
%o A344179 search_up_to = 2^22;
%o A344179 A076934(n) = for(k=2, oo , if(n%k, return(n), n /= k));
%o A344179 A093411(n) = if(!n,n, if(n%2, n, A093411(A076934(n))));
%o A344179 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
%o A344179 v001013 = A001013list(search_up_to);
%o A344179 A001013(n) = v001013[n];
%o A344179 isA344179(n) = if(v001013[#v001013]<n,-(1/0),((1!=A093411(n))&&vecsearch(v001013,n)));
%o A344179 for(n=1,search_up_to,if(isA344179(n),print1(n,", ")));
%Y A344179 Setwise difference of A001013 and A344181.
%Y A344179 Cf. A000142, A055874, A076934, A093411.
%K A344179 nonn
%O A344179 1,1
%A A344179 _Antti Karttunen_, May 18 2021