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Indices k such that A124652(k) is prime.
3

%I #19 May 05 2024 19:52:56

%S 2,3,5,11,12,20,24,28,29,33,42,43,53,58,67,78,93,98,104,105,109,112,

%T 118,125,126,137,141,145,146,162,174,182,185,187,188,195,200,223,224,

%U 231,232,239,246,249,252,255,259,264,271,275,283,286,287,296,298,300,326

%N Indices k such that A124652(k) is prime.

%C Analogous to A111238, a sequence which instead pertains to A109890.

%H Michael De Vlieger, <a href="/A372009/b372009.txt">Table of n, a(n) for n = 1..2500</a>

%H Michael De Vlieger, <a href="/A372009/a372009.png">Log log scatterplot of A124652(n)</a>, n = 1..25000, showing primes in red.

%F Proper subset of A372028.

%e Let b(x) = A124652(x).

%e Table of first terms.

%e n a(n) b(a(n))

%e -----------------

%e 1 2 2

%e 2 3 3

%e 3 5 5

%e 4 11 11

%e 5 12 7

%e 6 20 31

%e 7 24 13

%e 8 28 19

%e 9 29 17

%e 10 33 37

%e 11 42 29

%e 12 43 41

%e ...

%t nn = 300; c[_] := False;

%t rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];

%t f[x_] := Select[Range[x], Divisible[x, rad[#]] &];

%t Array[Set[{a[#], c[#]}, {#, True}] &, 2]; s = a[1] + a[2];

%t {2}~Join~Reap[Do[r = f[s]; k = SelectFirst[r, ! c[#] &];

%t If[PrimeQ[k], Sow[i]]; c[k] = True;

%t s += k, {i, 3, nn}] ][[-1, 1]]

%Y Cf. A124652, A372028, A372284.

%K nonn

%O 1,1

%A _Michael De Vlieger_, Apr 29 2024