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 A344179 Jordan-Polya numbers (A001013) not in A344181. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 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()); my(v=, 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]

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Last modified October 26 13:09 EDT 2021. Contains 348267 sequences. (Running on oeis4.)