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A363134
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Positive integers whose multiset of prime indices satisfies: (length) = 2*(minimum).
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3
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4, 6, 10, 14, 22, 26, 34, 38, 46, 58, 62, 74, 81, 82, 86, 94, 106, 118, 122, 134, 135, 142, 146, 158, 166, 178, 189, 194, 202, 206, 214, 218, 225, 226, 254, 262, 274, 278, 297, 298, 302, 314, 315, 326, 334, 346, 351, 358, 362, 375, 382, 386, 394, 398, 422, 441
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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.
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LINKS
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FORMULA
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EXAMPLE
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The terms together with their prime indices begin:
4: {1,1} 94: {1,15} 214: {1,28}
6: {1,2} 106: {1,16} 218: {1,29}
10: {1,3} 118: {1,17} 225: {2,2,3,3}
14: {1,4} 122: {1,18} 226: {1,30}
22: {1,5} 134: {1,19} 254: {1,31}
26: {1,6} 135: {2,2,2,3} 262: {1,32}
34: {1,7} 142: {1,20} 274: {1,33}
38: {1,8} 146: {1,21} 278: {1,34}
46: {1,9} 158: {1,22} 297: {2,2,2,5}
58: {1,10} 166: {1,23} 298: {1,35}
62: {1,11} 178: {1,24} 302: {1,36}
74: {1,12} 189: {2,2,2,4} 314: {1,37}
81: {2,2,2,2} 194: {1,25} 315: {2,2,3,4}
82: {1,13} 202: {1,26} 326: {1,38}
86: {1,14} 206: {1,27} 334: {1,39}
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Length[prix[#]]==2*Min[prix[#]]&]
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CROSSREFS
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Partitions of this type are counted by A237757.
Removing the factor 2 gives A324522.
A360005 gives twice median of prime indices.
Cf. A000961, A006141, A046660, A051293, A106529, A111907, A237755, A237824, A327482, A361860, A361861, A362050.
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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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