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A365413 a(1) = 2, a(n) = k - 1, where k is the least number greater than a(n-1) such that rad(k) | a(n-1), where rad(n) = A007947(n).

%I A365413 #20 Nov 19 2023 10:33:37
%S A365413 2,3,8,15,24,26,31,960,971,942840,944783,946728,948675,950624,952575,
%T A365413 954528,956483,958440,959999,2229048,2232035,2235024,2238015,2241008,
%U A365413 2244003,2247000,2249999,2253000,2256003,2259008,2262015,2265024,2268035,2271048,2274063,2277080,2280099
%N A365413 a(1) = 2, a(n) = k - 1, where k is the least number greater than a(n-1) such that rad(k) | a(n-1), where rad(n) = A007947(n).
%F A365413 a(n) = A289280(a(n-1)) - 1 for n > 1.
%e A365413 a(2) = 3 since 4 is the smallest k > a(1) such that rad(k) | a(1), and 4 - 1 = 3.
%e A365413 a(3) = 8 since 9 is the least k > a(2) such that rad(k) | a(2), and 9 - 1 = 8.
%e A365413 a(4) = 15 since 16 is the least k > a(3) such that rad(k) | a(3), and 16 - 1 = 15, etc.
%t A365413 rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
%t A365413 NestList[(k = # + 1; While[! Divisible[#, rad[k]], k++]; k - 1) &, 2, 20]
%Y A365413 Cf. A007947, A289280, A365324.
%K A365413 nonn,hard
%O A365413 1,1
%A A365413 _Michael De Vlieger_, Nov 15 2023