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A326537 MM-numbers of multiset partitions where each part has a different average. 11
1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 51, 53, 55, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 106, 107, 109, 110 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
These are numbers where each prime index has a different average 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 each part has a different average, preceded by their MM-numbers, begins:
1: {}
2: {{}}
3: {{1}}
5: {{2}}
6: {{},{1}}
7: {{1,1}}
10: {{},{2}}
11: {{3}}
13: {{1,2}}
14: {{},{1,1}}
15: {{1},{2}}
17: {{4}}
19: {{1,1,1}}
22: {{},{3}}
23: {{2,2}}
26: {{},{1,2}}
29: {{1,3}}
30: {{},{1},{2}}
31: {{5}}
33: {{1},{3}}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], UnsameQ@@Mean/@primeMS/@primeMS[#]&]
CROSSREFS
Sequence in context: A325399 A167171 A087008 * A302798 A294472 A077337
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 12 2019
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)