OFFSET
1,2
COMMENTS
An initial interval is a set {1,2,...,n} for some n >= 0.
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
EXAMPLE
The initial terms and corresponding multisets of multisets:
1: {}
2: {{}}
3: {{1}}
4: {{},{}}
6: {{},{1}}
8: {{},{},{}}
9: {{1},{1}}
12: {{},{},{1}}
13: {{1,2}}
16: {{},{},{},{}}
18: {{},{1},{1}}
24: {{},{},{},{1}}
26: {{},{1,2}}
27: {{1},{1},{1}}
32: {{},{},{},{},{}}
36: {{},{},{1},{1}}
39: {{1},{1,2}}
48: {{},{},{},{},{1}}
52: {{},{},{1,2}}
54: {{},{1},{1},{1}}
64: {{},{},{},{},{},{}}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
chinQ[y_]:=y==Range[Length[y]];
Select[Range[100], And@@chinQ/@primeMS/@primeMS[#]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 12 2022
STATUS
approved