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Least integer m whose largest prime factor > m^(n/(n+1)).
1

%I #8 May 12 2023 21:36:32

%S 6,10,22,34,74,134,262,514,1042,2062,4106,8198,16418,32822,65542,

%T 131074,262202,524294,1048618,2097166,4194338,8388638,16777234,

%U 33554518,67108934,134217758,268435514,536870918,1073741846,2147483654

%N Least integer m whose largest prime factor > m^(n/(n+1)).

%C a(n) > 2^(n+1); in fact a(n) = 2 * first prime which exceeds 2^n.

%F a(n) = 2 * A014210(n).

%t k = 2; Do[ While[ PrimeQ[ k ] || FactorInteger[ k ] [[ -1, 1 ] ] <= k^(n/(n + 1)), k++ ]; Print[ k ], {n, 1, 35} ]

%Y Cf. A014210.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Aug 14 2001