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a(n) = least prime factor of A024411(n).
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%I #8 Feb 04 2024 18:29:38

%S 2,2,3,2,3,2,2,3,2,3,2,5,2,3,3,2,2,5,3,2,2,3,5,2,2,2,3,2,3,5,2,7,2,3,

%T 2,3,2,7,3,2,2,3,5,3,2,2,5,2,3,2,7,2,3,2,2,5,3,2,3,2,5,2,3,2,3,2,2,3,

%U 7,2,5,3,2,3,5,2,7,3,2,3,2,3,2,5,2,3

%N a(n) = least prime factor of A024411(n).

%C Conjecture: every prime occurs infinitely many times.

%e Factorizations of for the first four terms of A024411 are given by

%e 20 = 2 * 2 * 5; 28 = 2 * 2 * 7; 33 = 3 * 13; 36 = 2*2*3*3;

%e so that (a(1), a(2), a(3), a(4)) = (2, 2, 3, 2).

%e Corner of array whose n-th row shows the numbers n such that a(n) = n-th prime:

%e 1 2 4 6 7 9 11

%e 3 5 8 10 14 15 19

%e 12 18 23 30 43 47 56

%e 32 38 51 69 77 94 107

%t readOEISbFile[bNumber_] := ToExpression[ToString[Map[StringReplace[#,

%t FromCharacterCode[32] -> FromCharacterCode[44]] &,

%t Map[Most[#] &, Cases[Map[{#, StringFreeQ[StringTake[#, 1],

%t Except[Apply[Alternatives, Flatten[{Map[ToString[#] &, Range[10] - 1],

%t FromCharacterCode[45], FromCharacterCode[8722], "+"}]]]]} &,

%t Map[StringDrop[StringDrop[#, 1], -1] &, DeleteCases[

%t Map[ToString[{#}] &, Import[If[Head[bNumber] === Integer,

%t "http://oeis.org/" <> "A" <> # <> "/b" <> # <> ".txt" &[

%t StringTrim[StringReplace[ToString[PadLeft[IntegerDigits[bNumber], 6]],

%t FromCharacterCode[{44, 32}] -> ""], "{" | "}"]],

%t bNumber], "List"]], "{}"]]], {_, True}]]]]]

%t s = readOEISbFile["http://oeis.org/A024411/b024411.txt"];

%t (* s = 10000 terms of A024411 from b-file *)

%t t = Map[Last, s]; u = Take[t, 1000];

%t f[n_] := FactorInteger[n][[1, 1]]; Join[{1}, Array[f, 120, 2]]; v = Map[f, u]

%t (* _Peter J. C. Moses_, Feb 03 2024 *)

%Y Cf. A000040, A018252, A024411.

%K nonn

%O 1,1

%A _Clark Kimberling_, Feb 03 2024