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 A302597 Squarefree numbers whose prime indices are powers of a common prime number. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A prime index of n is a number m such that prime(m) divides n. LINKS EXAMPLE 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}} MATHEMATICA primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[100], SameQ@@Join@@primeMS/@primeMS[#]&&SquareFreeQ[#]&] CROSSREFS Cf. A000961, A001222, A003963, A005117, A007716, A056239, A275024, A047966, A281113, A296134, A301766, A302242, A302243. Sequence in context: A073328 A119988 A087005 * A240101 A032892 A031941 Adjacent sequences:  A302594 A302595 A302596 * A302598 A302599 A302600 KEYWORD nonn AUTHOR Gus Wiseman, Apr 10 2018 STATUS approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)