Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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