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A366847
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Numbers whose halved even prime indices are nonempty and relatively prime.
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4
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3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 91, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174
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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.
Consists of powers of 2 times elements of the odd restriction A366849.
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LINKS
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EXAMPLE
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The even prime indices of 91 are {4,6}, halved {2,3}, which are relatively prime, so 91 is in the sequence.
The prime indices of 665 are {3,4,8}, even {4,8}, halved {2,4}, which are not relatively prime, so 665 is not in the sequence.
The terms together with their prime indices begin:
3: {2}
6: {1,2}
9: {2,2}
12: {1,1,2}
15: {2,3}
18: {1,2,2}
21: {2,4}
24: {1,1,1,2}
27: {2,2,2}
30: {1,2,3}
33: {2,5}
36: {1,1,2,2}
39: {2,6}
42: {1,2,4}
45: {2,2,3}
48: {1,1,1,1,2}
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MATHEMATICA
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Select[Range[100], GCD@@Select[PrimePi/@First/@FactorInteger[#], EvenQ]/2==1&]
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CROSSREFS
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The partitions with these ranks are counted by A366845.
Cf. A000720, A055396, A061395, A066208, A168532, A302696, A302697, A325698, A366842, A366843, A366844, A366848.
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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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