Problems & Puzzles: Puzzles

 Puzzle 874.Consecutive integers with increasing or non decreasing quantity of divisors Fred Schneider recently sent the following puzzle proposal: I had an idea for a couple of new sequences.  I believe they haven't been done before.  I can provide more terms if necessary   Consecutive numbers which have an increasing (>) or non-decreasing (>=) number of divisors.   For example:   3 has 2 divisors.  4 has 3 5 has 2.  So, 3-4 is a sequence of length 2. (n, t) n is the first number, t is the length of the sequence Increasing: 1) 2 2) 3, 4 3) 73-75 4) 61-64 5) 35221-35225 6) 11371-11376 Non-decreasing: 1) 4 2) 5,  6 3) 2, 3, 4 4) 13-16 5) 1613-1617 6) 241-246 These are now drafts in OEIS: A284596- Increasing; A284597 - Non-decreasing ...Shoot, similar sequences have already been created.  I guess it's worth still trying to extend them A075028 - increasing A075046 - non-decreasing Q1.Would you like to extend these sequences.

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