OFFSET
0,2
COMMENTS
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. The multiset of multisets with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of 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}}.
FORMULA
a(n) = A329558(n + 1)/2.
EXAMPLE
The sequence of terms together with their corresponding systems begins:
1: {}
3: {{1}}
15: {{1},{2}}
165: {{1},{2},{3}}
2145: {{1},{2},{3},{1,2}}
36465: {{1},{2},{3},{1,2},{4}}
1057485: {{1},{2},{3},{1,2},{4},{1,3}}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
dae=Select[Range[10000], SquareFreeQ[#]&&And@@SquareFreeQ/@primeMS[#]&&FreeQ[primeMS[#], 1]&];
Table[dae[[Position[PrimeOmega/@dae, k][[1, 1]]]], {k, First[Split[Union[PrimeOmega/@dae], #2==#1+1&]]}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 17 2019
STATUS
approved