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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
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.
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]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 18 2019
STATUS
approved