%I #20 Nov 19 2023 10:33:40

%S 2,5,26,33,82,129,244,257,66050,78126,78733,79508,81797,271442,524289,

%T 531442,551369,571788,580609,707282,1048577,1419858,1431645,1476226,

%U 1620897,1712422,2097153,2146690,2151297,2505890,2560001,11082242,16777217

%N 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 a(n) = A289280(a(n-1)) + 1 for n > 1.

%e a(2) = 5 since the least k > a(1) such that rad(k) | a(1) is 4, and 4 + 1 = 5.

%e a(3) = 26 since the least k > a(2) such that rad(k) | a(2) is 25, and 25 + 1 = 26.

%e a(4) = 33 since the smallest k > 26 such that rad(k) | 26 is 32, and 32 + 1 = 33, etc.

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

%t NestList[(k = # + 1; While[! Divisible[#, rad[k]], k++]; k + 1) &, 2, 20]

%Y Cf. A007947, A289280, A365413.

%K nonn,hard

%O 1,1

%A _Michael De Vlieger_, Nov 15 2023