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A367860
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Sum of the multiset multiplicity cokernel (in which each multiplicity becomes the greatest element of that multiplicity) of the prime indices of n.
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3
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0, 1, 2, 1, 3, 4, 4, 1, 2, 6, 5, 3, 6, 8, 6, 1, 7, 3, 8, 4, 8, 10, 9, 3, 3, 12, 2, 5, 10, 9, 11, 1, 10, 14, 8, 4, 12, 16, 12, 4, 13, 12, 14, 6, 5, 18, 15, 3, 4, 4, 14, 7, 16, 3, 10, 5, 16, 20, 17, 7, 18, 22, 6, 1, 12, 15, 19, 8, 18, 12, 20, 3, 21, 24, 5, 9, 10
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OFFSET
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1,3
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COMMENTS
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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.
We define the multiset multiplicity cokernel MMC(m) of a multiset m by the following property, holding for all distinct multiplicities k >= 1. If S is the set of elements of multiplicity k in m, then max(S) has multiplicity |S| in MMC(m). For example, MMC({1,1,2,2,3,4,5}) = {2,2,5,5,5}, and MMC({1,2,3,4,5,5,5,5}) = {4,4,4,4,5}. As an operation on multisets MMC is represented by A367858, and as an operation on their ranks it is represented by A367859.
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LINKS
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EXAMPLE
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The multiset multiplicity cokernel of {1,2,2,3} is {2,3,3}, so a(90) = 8.
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MATHEMATICA
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mmc[q_]:=With[{mts=Length/@Split[q]}, Sort[Table[Max@@Select[q, Count[q, #]==i&], {i, mts}]]];
Table[Total[mmc[PrimePi/@Join@@ConstantArray@@@If[n==1, {}, FactorInteger[n]]]], {n, 100}]
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CROSSREFS
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Positions of 1's are A000079 without 1.
Cf. A000720, A051904, A055396, A061395, A071625, A072774, A130091, A367580, A175781, A367582, A367584.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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