A365324 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).
2, 5, 26, 33, 82, 129, 244, 257, 66050, 78126, 78733, 79508, 81797, 271442, 524289, 531442, 551369, 571788, 580609, 707282, 1048577, 1419858, 1431645, 1476226, 1620897, 1712422, 2097153, 2146690, 2151297, 2505890, 2560001, 11082242, 16777217
Offset: 1
Examples
a(2) = 5 since the least k > a(1) such that rad(k) | a(1) is 4, and 4 + 1 = 5. a(3) = 26 since the least k > a(2) such that rad(k) | a(2) is 25, and 25 + 1 = 26. a(4) = 33 since the smallest k > 26 such that rad(k) | 26 is 32, and 32 + 1 = 33, etc.
Programs
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Mathematica
rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; NestList[(k = # + 1; While[! Divisible[#, rad[k]], k++]; k + 1) &, 2, 20]
Formula
a(n) = A289280(a(n-1)) + 1 for n > 1.