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A324855 Lexicographically earliest sequence containing 2 and all squarefree numbers > 2 whose prime indices already belong to the sequence. 2

%I #10 Mar 23 2019 02:37:19

%S 2,3,5,11,15,31,33,47,55,93,127,137,141,155,165,211,235,257,341,381,

%T 411,465,487,517,633,635,685,705,709,771,773,811,907,977,1023,1055,

%U 1285,1297,1397,1457,1461,1483,1507,1551,1621,1705,1905,2055,2127,2293,2319

%N Lexicographically earliest sequence containing 2 and all squarefree numbers > 2 whose prime indices already belong to the sequence.

%C 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.

%H Robert Israel, <a href="/A324855/b324855.txt">Table of n, a(n) for n = 1..1567</a>

%H Gus Wiseman, <a href="/A324855/a324855_1.png">The rooted identity trees whose Matula-Goebel numbers are the first 64 terms</a>.

%e The sequence of terms together with their prime indices begins:

%e 2: {1}

%e 3: {2}

%e 5: {3}

%e 11: {5}

%e 15: {2,3}

%e 31: {11}

%e 33: {2,5}

%e 47: {15}

%e 55: {3,5}

%e 93: {2,11}

%e 127: {31}

%e 137: {33}

%e 141: {2,15}

%e 155: {3,11}

%e 165: {2,3,5}

%e 211: {47}

%e 235: {3,15}

%e 257: {55}

%e 341: {5,11}

%e 381: {2,31}

%p S:= {2}: count:= 1:

%p for n from 3 by 2 while count < 100 do

%p F:= ifactors(n)[2];

%p if max(map(t -> t[2],F))=1 and {seq(numtheory:-pi(t[1]),t=F)} subset S then

%p S:= S union {n}; count:= count+1;

%p fi

%p od:

%p sort(convert(S,list)); # _Robert Israel_, Mar 22 2019

%t aQ[n_]:=Switch[n,1,False,2,True,_?(!SquareFreeQ[#]&),False,_,And@@Cases[FactorInteger[n],{p_,k_}:>aQ[PrimePi[p]]]];

%t Select[Range[1000],aQ]

%Y Cf. A000002, A000720, A001462, A079254, A109298, A112798, A276625, A290822.

%Y Cf. A324697, A324698, A324736, A324748, A324753, A324843, A324850, A324854.

%Y Contains A007097 except for 1.

%K nonn

%O 1,1

%A _Gus Wiseman_, Mar 18 2019

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)