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 A326536 MM-numbers of multiset partitions where every part has the same average. 9
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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}}. LINKS EXAMPLE The sequence of multiset partitions where every part has the same average, 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: {{},{},{},{},{}} MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[100], SameQ@@Mean/@primeMS/@primeMS[#]&] CROSSREFS Cf. A038041, A051293, A112798, A302242, A320324, A326512, A326515, A326520, A326533, A326534, A326535, A326537. Sequence in context: A014567 A324769 A328867 * A322902 A302040 A302036 Adjacent sequences:  A326533 A326534 A326535 * A326537 A326538 A326539 KEYWORD nonn AUTHOR Gus Wiseman, Jul 12 2019 STATUS approved

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Last modified February 23 16:22 EST 2020. Contains 332177 sequences. (Running on oeis4.)