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A372028 Numbers k such that A124652(k) divides A372111(k-1).

%I A372028 #73 May 05 2024 19:55:09
%S A372028 3,5,7,11,12,13,15,16,17,18,20,22,24,26,27,28,29,30,31,33,40,41,42,43,
%T A372028 44,46,49,50,51,53,55,58,59,60,62,63,64,66,67,68,69,70,71,72,73,78,79,
%U A372028 80,92,93,95,98,101,102,103,104,105,107,109,111,112,115,116,117
%N A372028 Numbers k such that A124652(k) divides A372111(k-1).
%C A372028 Contains A372009(m), m > 1.
%C A372028 For k in this sequence, A124652(k) has the same relationship with A372111(k-1) as A109890(i) has with A109735(i-1) for i > 2.
%H A372028 Michael De Vlieger, <a href="/A372028/b372028.txt">Table of n, a(n) for n = 1..10000</a>
%H A372028 Michael De Vlieger, <a href="/A372028/a372028.png">Log log scatterplot of A124652(n)</a>, n = 1..10^5, showing A124652(a(n)) in green, but A124652(a(n)) that are prime in red.
%F A372028 A124652(a(n)) is a number in row A372111(a(n)-1) of A027750.
%e A372028 Let b(x) = A124652(x) and s(x) = A372111(x), where A372111 contains partial sums of A124652.
%e A372028 a(1) = 3 since b(3) = 3, a divisor of s(2) = 3.
%e A372028 a(2) = 5 since b(5) = 5, a divisor of s(4) = 10.
%e A372028 a(3) = 7 since b(7) = 6, a divisor of s(6) = 24, etc.
%t A372028 nn = 120; c[_] := False;
%t A372028 rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
%t A372028 f[x_] := Select[Range[x], Divisible[x, rad[#]] &];
%t A372028 Array[Set[{a[#], c[#]}, {#, True}] &, 2]; s = a[1] + a[2];
%t A372028 Reap[Do[r = f[s]; k = SelectFirst[r, ! c[#] &];
%t A372028   If[Divisible[s, k], Sow[i]]; c[k] = True;
%t A372028   s += k, {i, 3, nn}] ][[-1, 1]]
%Y A372028 Cf. A007947, A027750, A109735, A109890, A124652, A372009, A372111, A372399.
%K A372028 nonn
%O A372028 1,1
%A A372028 _Michael De Vlieger_, May 05 2024