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A302597
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Squarefree numbers whose prime indices are powers of a common prime number.
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0
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1, 2, 3, 5, 6, 7, 10, 11, 14, 17, 19, 21, 22, 23, 31, 34, 38, 41, 42, 46, 53, 57, 59, 62, 67, 82, 83, 97, 103, 106, 109, 114, 115, 118, 127, 131, 133, 134, 157, 159, 166, 179, 191, 194, 206, 211, 218, 227, 230, 241, 254, 262, 266, 277, 283, 311, 314, 318, 331
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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.
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LINKS
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EXAMPLE
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Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set systems.
01: {}
02: {{}}
03: {{1}}
05: {{2}}
06: {{},{1}}
07: {{1,1}}
10: {{},{2}}
11: {{3}}
14: {{},{1,1}}
17: {{4}}
19: {{1,1,1}}
21: {{1},{1,1}}
22: {{},{3}}
23: {{2,2}}
31: {{5}}
34: {{},{4}}
38: {{},{1,1,1}}
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MATHEMATICA
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primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], SameQ@@Join@@primeMS/@primeMS[#]&&SquareFreeQ[#]&]
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CROSSREFS
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Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A047966, A281113, A296134, A301766, A302242, A302243.
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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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