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A356232
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Numbers whose prime indices are all odd and cover an initial interval of odd positive integers.
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16
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1, 2, 4, 8, 10, 16, 20, 32, 40, 50, 64, 80, 100, 110, 128, 160, 200, 220, 250, 256, 320, 400, 440, 500, 512, 550, 640, 800, 880, 1000, 1024, 1100, 1210, 1250, 1280, 1600, 1760, 1870, 2000, 2048, 2200, 2420, 2500, 2560, 2750, 3200, 3520, 3740, 4000, 4096, 4400
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OFFSET
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1,2
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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 positions of first appearances of rows in A356226.
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
1: {}
2: {1}
4: {1,1}
8: {1,1,1}
10: {1,3}
16: {1,1,1,1}
20: {1,1,3}
32: {1,1,1,1,1}
40: {1,1,1,3}
50: {1,3,3}
64: {1,1,1,1,1,1}
80: {1,1,1,1,3}
100: {1,1,3,3}
110: {1,3,5}
128: {1,1,1,1,1,1,1}
160: {1,1,1,1,1,3}
200: {1,1,1,3,3}
220: {1,1,3,5}
250: {1,3,3,3}
256: {1,1,1,1,1,1,1,1}
320: {1,1,1,1,1,1,3}
400: {1,1,1,1,3,3}
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
normQ[m_]:=Or[m=={}, Union[m]==Range[Max[m]]];
Select[Range[1000], normQ[(primeMS[#]+1)/2]&]
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CROSSREFS
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The partitions with these Heinz numbers are counted by A053251.
This is the odd restriction of A055932.
A subset of A066208 (numbers with all odd prime indices).
This is the sorted version of A356603.
These are the positions of first appearances of rows in A356226. Other statistics are:
- positions of first appearances: A356232 (this sequence)
A003963 multiplies together the prime indices.
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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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