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).

2, 3, 8, 15, 24, 26, 31, 960, 971, 942840, 944783, 946728, 948675, 950624, 952575, 954528, 956483, 958440, 959999, 2229048, 2232035, 2235024, 2238015, 2241008, 2244003, 2247000, 2249999, 2253000, 2256003, 2259008, 2262015, 2265024, 2268035, 2271048, 2274063, 2277080, 2280099

Offset: 1

Author

Michael De Vlieger, Nov 15 2023

Keywords

• nonn
• hard

Examples

			a(2) = 3 since 4 is the smallest k > a(1) such that rad(k) | a(1), and 4 - 1 = 3.
a(3) = 8 since 9 is the least k > a(2) such that rad(k) | a(2), and 9 - 1 = 8.
a(4) = 15 since 16 is the least k > a(3) such that rad(k) | a(3), and 16 - 1 = 15, etc.
		

Crossrefs

Cf. A007947, A289280, A365324.

Programs

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.