A338759 a(n+1) is the maximum number of groups which can be built from the terms in this sequence so far and using each term only once which result in a(n) as their product with a(1) = 1.

1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 2, 2, 3, 2, 4, 4, 5, 2, 5, 3, 3, 4, 6, 6, 7, 1, 7, 2, 6, 8, 5, 4, 8, 7, 3, 5, 5, 6, 10, 7, 4, 9, 3, 6, 12, 13, 1, 8, 9, 5, 7, 5, 8, 10, 8, 11, 1, 9, 6, 13, 2, 7, 6, 14, 7, 7, 8, 12, 15, 7, 9, 7, 10, 10, 11, 2, 8, 13, 3, 7, 11, 3, 8, 14

Offset: 1

Author

S. Brunner, Nov 07 2020

Keywords

• nonn

Comments

This sequence is a variant of A332518 without the requirement that all factors have to be consecutive numbers.

Examples

			To get a(n+1), count how many times a(n) appears in the sequence.
For 1 and primes, this is already a(n+1).
For prime squares, also count how many times the prime factor appears in the sequence, divide it by 2 and round it down.
For example, the next term after a(43) = 9 is 3, because 9 appeared 1 time (at a(43) itself) and 3 appeared 5 times, which can arranged in 2 groups of 3 X 3.
For semiprimes, count how many times the semiprime itself appears in the sequence. Then count how many times the 2 factors appear and add the smallest number.
For example, the next term after a(30) = 6 is 8, because 6 appeared 4 times and the factors 2 and 3 appeared 6 and 4 times. We can build 4 groups of 2 X 3 of them.
		

Links

• S. Brunner, Table of n, a(n) for n = 1..10000
• S. Brunner, List for n = 1..10000 together with the factorizations.
• S. Brunner, Python program.

Crossrefs

Cf. A001222 (bigomega), A162247 (all factorizations of n).

Cf. A332518.