Revision History for A326536
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
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#6 by Susanna Cuyler at Sat Jul 13 09:13:10 EDT 2019
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#5 by Gus Wiseman at Fri Jul 12 20:56:28 EDT 2019
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#4 by Gus Wiseman at Fri Jul 12 20:55:20 EDT 2019
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| LINKS
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Gus Wiseman, <a href="/A038041/a038041.txt">Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.</a>
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| EXAMPLE
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The sequence of multiset partitions where every part satisfyinghas the conditionsame average, preceded by their MM-numbers , begins:
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| CROSSREFS
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Cf. A038041, A051293, A112798, A302242, A320324, A326512, A326515, A326520, A326533, A326534, A326535, A326537.
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#3 by Gus Wiseman at Fri Jul 12 00:55:41 EDT 2019
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| CROSSREFS
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Cf. A051293, A112798, A302242, A320324, A326512, A326515, A326520, A326533, A326534, A326535, A326537.
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#2 by Gus Wiseman at Fri Jul 12 00:49:08 EDT 2019
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| NAME
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allocatedMM-numbers of multiset partitions where every part has forthe Gussame Wisemanaverage.
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| DATA
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1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 57, 59, 61, 63, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 115, 121, 125, 127, 128, 131, 133, 137, 139, 145, 147, 149, 151, 157, 159, 163, 167
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| OFFSET
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1,2
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| COMMENTS
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First differs from A322902 in having 145.
These are numbers where each prime index has the same 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}}.
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| EXAMPLE
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The sequence of multiset partitions satisfying the condition 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}}
21: {{1},{1,1}}
23: {{2,2}}
25: {{2},{2}}
27: {{1},{1},{1}}
29: {{1,3}}
31: {{5}}
32: {{},{},{},{},{}}
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| MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], SameQ@@Mean/@primeMS/@primeMS[#]&]
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| CROSSREFS
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Cf. A112798, A302242, A320324, A326512, A326515, A326520, A326533, A326534, A326535, A326537.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Gus Wiseman, Jul 12 2019
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| STATUS
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approved
editing
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#1 by Gus Wiseman at Thu Jul 11 18:56:52 EDT 2019
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| NAME
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allocated for Gus Wiseman
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| KEYWORD
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allocated
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| STATUS
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approved
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