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A324517
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Numbers > 1 where the maximum prime index equals the number of prime factors minus the number of distinct prime factors.
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19
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4, 24, 27, 36, 54, 80, 200, 224, 240, 360, 405, 500, 540, 600, 625, 672, 675, 704, 784, 810, 900, 1008, 1120, 1125, 1250, 1350, 1500, 1512, 1664, 1701, 1875, 2112, 2250, 2268, 2352, 2744, 2800, 3168, 3360, 3402, 3520, 3528, 3750, 3872, 3920, 3969, 4352, 4752
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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.
Also Heinz numbers of the integer partitions enumerated by A324518. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
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LINKS
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FORMULA
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EXAMPLE
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The sequence of terms together with their prime indices begins:
4: {1,1}
24: {1,1,1,2}
27: {2,2,2}
36: {1,1,2,2}
54: {1,2,2,2}
80: {1,1,1,1,3}
200: {1,1,1,3,3}
224: {1,1,1,1,1,4}
240: {1,1,1,1,2,3}
360: {1,1,1,2,2,3}
405: {2,2,2,2,3}
500: {1,1,3,3,3}
540: {1,1,2,2,2,3}
600: {1,1,1,2,3,3}
625: {3,3,3,3}
672: {1,1,1,1,1,2,4}
675: {2,2,2,3,3}
704: {1,1,1,1,1,1,5}
784: {1,1,1,1,4,4}
810: {1,2,2,2,2,3}
900: {1,1,2,2,3,3}
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MATHEMATICA
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Select[Range[2, 1000], With[{f=FactorInteger[#]}, PrimePi[f[[-1, 1]]]==Total[Last/@f]-Length[f]]&]
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CROSSREFS
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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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