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%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
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