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A325326
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Heinz numbers of integer partitions covering an initial interval of positive integers with distinct multiplicities.
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14
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1, 2, 4, 8, 12, 16, 18, 24, 32, 48, 54, 64, 72, 96, 108, 128, 144, 162, 192, 256, 288, 324, 360, 384, 432, 486, 512, 540, 576, 600, 648, 720, 768, 864, 972, 1024, 1152, 1200, 1350, 1440, 1458, 1500, 1536, 1620, 1728, 1944, 2048, 2160, 2250, 2304, 2400, 2592
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OFFSET
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1,2
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COMMENTS
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The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
The enumeration of these partitions by sum is given by A320348.
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LINKS
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FORMULA
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Intersection of normal numbers (A055932) and numbers with distinct prime exponents (A130091).
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EXAMPLE
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The sequence of terms together with their prime indices begins:
1: {}
2: {1}
4: {1,1}
8: {1,1,1}
12: {1,1,2}
16: {1,1,1,1}
18: {1,2,2}
24: {1,1,1,2}
32: {1,1,1,1,1}
48: {1,1,1,1,2}
54: {1,2,2,2}
64: {1,1,1,1,1,1}
72: {1,1,1,2,2}
96: {1,1,1,1,1,2}
108: {1,1,2,2,2}
128: {1,1,1,1,1,1,1}
144: {1,1,1,1,2,2}
162: {1,2,2,2,2}
192: {1,1,1,1,1,1,2}
256: {1,1,1,1,1,1,1,1}
288: {1,1,1,1,1,2,2}
324: {1,1,2,2,2,2}
360: {1,1,1,2,2,3}
384: {1,1,1,1,1,1,1,2}
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MATHEMATICA
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normQ[n_Integer]:=n==1||PrimePi/@First/@FactorInteger[n]==Range[PrimeNu[n]];
Select[Range[100], normQ[#]&&UnsameQ@@Last/@FactorInteger[#]&]
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CROSSREFS
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Cf. A000837, A047966, A055932, A056239, A098859, A112798, A130091, A317081, A317089, A320348, A325329, A325337, A325369, A325372.
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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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