OFFSET
1,2
COMMENTS
First differs from A298538 in lacking 187.
These are numbers where each prime index has the same sum of prime indices. 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 multisystem with MM-number n is obtained by taking the multiset of prime indices of each prime index of n. For example, the prime indices of 78 are {1,2,6}, so the multiset multisystem with MM-number 78 is {{},{1},{1,2}}.
LINKS
EXAMPLE
The sequence of multiset partitions where every part has the same sum, preceded by their MM-numbers, begins:
1: {}
2: {{}}
3: {{1}}
4: {{},{}}
5: {{2}}
7: {{1,1}}
8: {{},{},{}}
9: {{1},{1}}
11: {{3}}
13: {{1,2}}
16: {{},{},{},{}}
17: {{4}}
19: {{1,1,1}}
23: {{2,2}}
25: {{2},{2}}
27: {{1},{1},{1}}
29: {{1,3}}
31: {{5}}
32: {{},{},{},{},{}}
35: {{2},{1,1}}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], SameQ@@Total/@primeMS/@primeMS[#]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 12 2019
STATUS
approved