All natural integers will appear sooner or later in the sequence - but mostly “later”! Indeed, the sequence increases very slowly: after 100000 terms the smallest term not yet present is 32.

Here is, in the same range, a sample of the count {term, occurrences} so far:

{1,192},{2,396},{3,618},{4,796},{5,1160},{6,1296},{7,2294},{8,2080},{9,2489},{10 ,2826},{11,3487},{12,1596},{13,2295},{14,1960},{15,2370},{16,2640},{17,4097},{18 ,2214},{19,4598},{20,2770},{21,3759},{22,4477},{23,5612},{24,4884},{25,5825},{26 ,6006},{27,6359},{28,4676},{29,5481},{30,3060},{31,1411},{32,0},{33,182},{34,0},{35 ,315},{36,0},{37,1221},{38,0},{39,214},{40,0},{41,1353},{42,0},{43,1183},{44,0},{45 ,0},{46,0},{47,1058},{48,0},{49,172},{50,0},{51,0},{52,0},{53,580}...

After 100000 terms, the first products that are not yet present are (the primes): 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,... and (the composites) 118, 122, 134,...

Here is again a sample so far (100000 terms computed) of {product, number of occurrences of the product}: