|
| |
|
|
A330664
|
|
Number of non-isomorphic balanced reduced multisystems of maximum depth whose degrees (atom multiplicities) are the weakly decreasing prime indices of n.
|
|
7
|
|
|
|
1, 1, 1, 1, 1, 2, 2, 1, 4, 5, 5, 7, 16, 16, 27, 2, 61, 33, 272, 27, 123, 61, 1385, 27, 78, 272, 95, 123, 7936, 362
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,6
|
|
|
COMMENTS
|
A balanced reduced multisystem is either a finite multiset, or a multiset partition with at least two parts, not all of which are singletons, of a balanced reduced multisystem.
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. A multiset whose multiplicities are the prime indices of n (such as row n of A305936) is generally not the same as the multiset of prime indices of n. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}.
|
|
|
LINKS
|
|
|
|
FORMULA
|
For n > 1, a(2^n) = a(prime(n)) = A000111(n - 1).
|
|
|
EXAMPLE
|
Non-isomorphic representatives of the a(n) multisystems for n = 2, 3, 6, 9, 10, 12 (commas and outer brackets elided):
1 11 {1}{12} {{1}}{{1}{22}} {{1}}{{1}{12}} {{1}}{{1}{23}}
{2}{11} {{11}}{{2}{2}} {{11}}{{1}{2}} {{11}}{{2}{3}}
{{1}}{{2}{12}} {{1}}{{2}{11}} {{1}}{{2}{13}}
{{12}}{{1}{2}} {{12}}{{1}{1}} {{12}}{{1}{3}}
{{2}}{{1}{11}} {{2}}{{1}{13}}
{{2}}{{3}{11}}
{{23}}{{1}{1}}
|
|
|
CROSSREFS
|
The non-maximal version is A330666.
The case of constant or strict atoms is A000111.
Non-isomorphic multiset partitions whose degrees are the prime indices of n are A318285.
Cf. A004114, A005121, A007716, A048816, A141268, A306186, A318846, A318848, A330470, A330474, A330663.
|
|
|
KEYWORD
|
nonn,more
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
