A356944 - OEIS

A356944

MM-numbers of multisets of gapless multisets of positive integers. Products of primes indexed by elements of A073491.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

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OFFSET

1,2

COMMENTS

A multiset is gapless if it covers an interval of positive integers. For example, {2,3,3,4} is gapless but {1,1,3,3} is not.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

We define the multiset of multisets with MM-number n to be formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. The size of this multiset of multisets is A302242(n). For example, the prime indices of 78 are {1,2,6}, so the multiset of multisets with MM-number 78 is {{},{1},{1,2}}.

LINKS

Table of n, a(n) for n=1..67.

Gus Wiseman, Counting and ranking classes of multiset partitions related to gapless multisets

EXAMPLE

The initial terms and corresponding multiset partitions:

1: {}

2: {{}}

3: {{1}}

4: {{},{}}

5: {{2}}

6: {{},{1}}

7: {{1,1}}