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 A320456 Numbers whose multiset multisystem spans an initial interval of positive integers. 14
 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 15, 16, 18, 19, 21, 24, 26, 27, 28, 30, 32, 35, 36, 37, 38, 39, 42, 45, 48, 49, 52, 53, 54, 56, 57, 60, 61, 63, 64, 65, 69, 70, 72, 74, 75, 76, 78, 81, 84, 89, 90, 91, 95, 96, 98, 104, 105, 106, 108, 111, 112, 113, 114, 117 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 n-th multiset multisystem 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 78th multiset multisystem is {{},{1},{1,2}}. LINKS EXAMPLE The sequence of terms together with their multiset multisystems begins:    1: {}    2: {{}}    3: {{1}}    4: {{},{}}    6: {{},{1}}    7: {{1,1}}    8: {{},{},{}}    9: {{1},{1}}   12: {{},{},{1}}   13: {{1,2}}   14: {{},{1,1}}   15: {{1},{2}}   16: {{},{},{},{}}   18: {{},{1},{1}}   19: {{1,1,1}}   21: {{1},{1,1}}   24: {{},{},{},{1}}   26: {{},{1,2}}   27: {{1},{1},{1}}   28: {{},{},{1,1}}   30: {{},{1},{2}}   32: {{},{},{},{},{}} MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; normQ[sys_]:=Or[Length[sys]==0, Union@@sys==Range[Max@@Max@@sys]]; Select[Range[100], normQ[primeMS/@primeMS[#]]&] CROSSREFS Cf. A001222, A003963, A034691, A034729, A055932, A056239, A112798, A255906, A290103, A302242, A305052. Cf. A320458, A320459, A320461, A320462, A320463, A320464, A320532, A320533. Sequence in context: A059325 A258938 A004763 * A239015 A030706 A285986 Adjacent sequences:  A320453 A320454 A320455 * A320457 A320458 A320459 KEYWORD nonn AUTHOR Gus Wiseman, Oct 13 2018 STATUS approved

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Last modified July 22 07:23 EDT 2019. Contains 325216 sequences. (Running on oeis4.)