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A353839
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Numbers whose prime indices do not have all distinct run-sums.
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24
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12, 40, 60, 63, 84, 112, 120, 126, 132, 144, 156, 204, 228, 252, 276, 280, 300, 315, 325, 336, 348, 351, 352, 360, 372, 420, 440, 444, 492, 504, 516, 520, 560, 564, 588, 630, 636, 650, 660, 675, 680, 693, 702, 708, 720, 732, 760, 780, 804, 819, 832, 840, 852
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OFFSET
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1,1
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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.
Every sequence can be uniquely split into a sequence of non-overlapping runs. For example, the runs of (2,2,1,1,1,3,2,2) are ((2,2),(1,1,1),(3),(2,2)), with sums (4,3,3,4).
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
12: {1,1,2}
40: {1,1,1,3}
60: {1,1,2,3}
63: {2,2,4}
84: {1,1,2,4}
112: {1,1,1,1,4}
120: {1,1,1,2,3}
126: {1,2,2,4}
132: {1,1,2,5}
144: {1,1,1,1,2,2}
156: {1,1,2,6}
204: {1,1,2,7}
228: {1,1,2,8}
252: {1,1,2,2,4}
276: {1,1,2,9}
280: {1,1,1,3,4}
300: {1,1,2,3,3}
315: {2,2,3,4}
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MATHEMATICA
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Select[Range[100], !UnsameQ@@Cases[FactorInteger[#], {p_, k_}:>k*PrimePi[p]]&]
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CROSSREFS
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A098859 counts partitions with distinct multiplicities, ranked by A130091.
A165413 counts distinct run-sums in binary expansion.
A351014 counts distinct runs in standard compositions.
A353832 represents taking run-sums of a partition, compositions A353847.
A353852 ranks compositions with all distinct run-sums, counted by A353850.
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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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