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 A324855 Lexicographically earliest sequence containing 2 and all squarefree numbers > 2 whose prime indices already belong to the sequence. 2
 2, 3, 5, 11, 15, 31, 33, 47, 55, 93, 127, 137, 141, 155, 165, 211, 235, 257, 341, 381, 411, 465, 487, 517, 633, 635, 685, 705, 709, 771, 773, 811, 907, 977, 1023, 1055, 1285, 1297, 1397, 1457, 1461, 1483, 1507, 1551, 1621, 1705, 1905, 2055, 2127, 2293, 2319 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Robert Israel, Table of n, a(n) for n = 1..1567 EXAMPLE The sequence of terms together with their prime indices begins:     2: {1}     3: {2}     5: {3}    11: {5}    15: {2,3}    31: {11}    33: {2,5}    47: {15}    55: {3,5}    93: {2,11}   127: {31}   137: {33}   141: {2,15}   155: {3,11}   165: {2,3,5}   211: {47}   235: {3,15}   257: {55}   341: {5,11}   381: {2,31} MAPLE S:= {2}: count:= 1: for n from 3 by 2 while count < 100 do   F:= ifactors(n)[2];   if max(map(t -> t[2], F))=1 and {seq(numtheory:-pi(t[1]), t=F)} subset S then      S:= S union {n}; count:= count+1;   fi od: sort(convert(S, list)); # Robert Israel, Mar 22 2019 MATHEMATICA aQ[n_]:=Switch[n, 1, False, 2, True, _?(!SquareFreeQ[#]&), False, _, And@@Cases[FactorInteger[n], {p_, k_}:>aQ[PrimePi[p]]]]; Select[Range[1000], aQ] CROSSREFS Cf. A000002, A000720, A001462, A079254, A109298, A112798, A276625, A290822. Cf. A324697, A324698, A324736, A324748, A324753, A324843, A324850, A324854. Contains A007097 except for 1. Sequence in context: A275913 A004680 A230147 * A316467 A282238 A004690 Adjacent sequences:  A324852 A324853 A324854 * A324856 A324857 A324858 KEYWORD nonn AUTHOR Gus Wiseman, Mar 18 2019 STATUS approved

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Last modified October 16 08:50 EDT 2019. Contains 328056 sequences. (Running on oeis4.)