recovery of A096113

[Richard Mathar]

A096113 seems to need some repair. The construction of the sequence
would start with the seeds 1 and 2 with no further products needed.
(Seeds are those smallest integers not yet in the list which are added after
the sorted products of any distinct factors of the numbers already in the list
have been added.) "Add" means put the number into the intermediate bag
of products which will be sorted and added once all products are collected.
 add 3 next seed
tst product 2 3 add 6
 sorted sequence 6 
 add 4 next seed
tst product 2 6 add 12
tst product 3 6 add 18
tst product 2 3 6 add 36
tst product 2 4 add 8
tst product 2 3 4 add 24
tst product 2 6 4 add 48
tst product 3 6 4 add 72
tst product 2 3 6 4 add 144
 sorted sequence 8 12 18 24 36 48 72 144 
  (18 missing in the current OEIS version)
 add 5 next seed
tst product 2 8 add 16
  (16 missing in the current OEIS version)
tst product 2 6 8 add 96
tst product 2 3 6 8 add 288
tst product 4 8 add 32
  (32 missing in the current OEIS version)
tst product 2 4 8 add 64
tst product 2 3 4 8 add 192
tst product 2 6 4 8 add 384
tst product 3 6 4 8 add 576
tst product 2 3 6 4 8 add 1152
tst product 3 6 12 add 216
tst product 2 3 6 12 add 432
tst product 3 6 4 12 add 864
tst product 2 3 6 4 12 add 1728
tst product 2 3 6 8 12 add 3456
tst product 2 4 8 12 add 768
tst product 2 3 4 8 12 add 2304
tst product 2 6 4 8 12 add 4608
tst product 3 6 4 8 12 add 6912
tst product 2 3 6 4 8 12 add 13824
tst product 3 18 add 54
tst product 2 3 18 add 108
tst product 3 6 18 add 324
tst product 2 3 6 18 add 648
tst product 3 6 4 18 add 1296
tst product 2 3 6 4 18 add 2592
tst product 2 3 6 8 18 add 5184
tst product 3 6 4 8 18 add 10368
tst product 2 3 6 4 8 18 add 20736
tst product 3 6 12 18 add 3888
tst product 2 3 6 12 18 add 7776
tst product 3 6 4 12 18 add 15552
tst product 2 3 6 4 12 18 add 31104
tst product 2 3 6 8 12 18 add 62208
tst product 2 3 4 8 12 18 add 41472
tst product 2 6 4 8 12 18 add 82944
tst product 3 6 4 8 12 18 add 124416
tst product 2 3 6 4 8 12 18 add 248832
tst product 2 4 8 24 add 1536
tst product 2 6 4 8 24 add 9216
tst product 2 3 6 4 8 24 add 27648
tst product 2 4 8 12 24 add 18432
tst product 2 3 4 8 12 24 add 55296
tst product 2 6 4 8 12 24 add 110592
tst product 3 6 4 8 12 24 add 165888
tst product 2 3 6 4 8 12 24 add 331776
tst product 2 3 6 4 8 18 24 add 497664
tst product 3 6 12 18 24 add 93312
tst product 2 3 6 12 18 24 add 186624
tst product 3 6 4 12 18 24 add 373248
tst product 2 3 6 4 12 18 24 add 746496
tst product 2 3 6 8 12 18 24 add 1492992
tst product 2 3 4 8 12 18 24 add 995328
tst product 2 6 4 8 12 18 24 add 1990656
tst product 3 6 4 8 12 18 24 add 2985984
tst product 2 3 6 4 8 12 18 24 add 5971968
tst product 3 18 36 add 1944
tst product 3 6 18 36 add 11664
tst product 2 3 6 18 36 add 23328
tst product 3 6 4 18 36 add 46656
tst product 3 6 12 18 36 add 139968
tst product 2 3 6 12 18 36 add 279936
tst product 3 6 4 12 18 36 add 559872
tst product 2 3 6 4 12 18 36 add 1119744
tst product 2 3 6 8 12 18 36 add 2239488
tst product 3 6 4 8 12 18 36 add 4478976
tst product 2 3 6 4 8 12 18 36 add 8957952
tst product 2 4 8 12 24 36 add 663552
tst product 2 6 4 8 12 24 36 add 3981312
tst product 2 3 6 4 8 12 24 36 add 11943936
tst product 2 3 6 4 8 18 24 36 add 17915904
tst product 3 6 12 18 24 36 add 3359232
tst product 2 3 6 12 18 24 36 add 6718464
tst product 3 6 4 12 18 24 36 add 13436928
tst product 2 3 6 4 12 18 24 36 add 26873856
tst product 2 3 6 8 12 18 24 36 add 53747712
tst product 2 3 4 8 12 18 24 36 add 35831808
tst product 2 6 4 8 12 18 24 36 add 71663616
tst product 3 6 4 8 12 18 24 36 add 107495424
tst product 2 3 6 4 8 12 18 24 36 add 214990848
tst product 2 4 8 48 add 3072
tst product 2 4 8 12 48 add 36864
tst product 2 6 4 8 12 48 add 221184
tst product 2 4 8 24 48 add 73728
tst product 2 6 4 8 24 48 add 442368
tst product 2 3 6 4 8 24 48 add 1327104
tst product 2 4 8 12 24 48 add 884736
tst product 2 3 4 8 12 24 48 add 2654208
tst product 2 6 4 8 12 24 48 add 5308416
tst product 3 6 4 8 12 24 48 add 7962624
tst product 2 3 6 4 8 12 24 48 add 15925248
tst product 2 3 6 4 8 18 24 48 add 23887872
tst product 2 3 4 8 12 18 24 48 add 47775744
tst product 2 6 4 8 12 18 24 48 add 95551488
tst product 3 6 4 8 12 18 24 48 add 143327232
tst product 2 3 6 4 8 12 18 24 48 add 286654464
tst product 2 3 6 4 8 12 18 36 48 add 429981696
tst product 2 4 8 12 24 36 48 add 31850496
tst product 2 6 4 8 12 24 36 48 add 191102976
tst product 2 3 6 4 8 12 24 36 48 add 573308928
tst product 2 3 6 4 8 18 24 36 48 add 859963392
tst product 3 6 12 18 24 36 48 add 161243136
tst product 2 3 6 12 18 24 36 48 add 322486272
tst product 3 6 4 12 18 24 36 48 add 644972544
tst product 2 3 6 4 12 18 24 36 48 add 1289945088
tst product 2 3 6 8 12 18 24 36 48 add 2579890176
tst product 2 3 4 8 12 18 24 36 48 add 1719926784
tst product 2 6 4 8 12 18 24 36 48 add 3439853568
tst product 3 6 4 8 12 18 24 36 48 add 5159780352
tst product 2 3 6 4 8 12 18 24 36 48 add 10319560704

etc...

The final sequence would start like
1,2,3,6,4,8,12,18,24,36,48,72,144,5,10,15,16,20,30,32,40,54,60,64,80,90,96,108,
120,160,180,192,216,240,270,288,320,324,360,384,432,480,540,576,648,720,768,
864,960,1080,1152,1296,1440,1536,1620,1728,1920,1944,2160,2304,2592,2880,3072,
3240,3456,3840,3888,4320,4608,5184,5760,6480,6912,7680,7776,8640,9216,9720,
10368,11520,11664,12960,13824,15360,15552,17280,18432,19440,20736,23040,23328,
25920,27648,31104,34560,36864,38880,41472,46080,46656,51840,55296,58320,62208,
69120,73728,77760,82944,92160,93312,103680,110592,116640,124416,138240,139968,
155520,165888,184320,186624,207360,221184,233280,248832,276480,279936,311040,
331776,368640,373248,414720,442368,466560,497664,552960,559872,622080,663552,
699840,746496,829440,839808,884736,933120,995328,1105920,1119744,1244160,
1327104,1399680,1492992,1658880,1679616,1866240,1990656,2211840,2239488,

Richard, http://www.strw.leidenuniv.nl/~mathar