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%I #16 Aug 01 2019 00:20:03
%S 2,4913,29410,96854,236916,484596,879483,1465239,2289183,3401984,
%T 4857388,6712006,9025131,11858570,15276512,19345406,24133846,29712478,
%U 36153913,43532644,51924974,61408954,72064316,83972419,97216198,111880113,128050105,145813554,165259239,186477301,209559205
%N Least integer k such that k^(1/3)/log(k) exceeds n.
%p A262059val := proc(k)
%p Digits := 100 ;
%p evalf(root[3](k)/log(k)) ;
%p end proc:
%p A262059lims := proc(n,lowk,highk)
%p local vallow, valhigh,midk,valmid ;
%p vallow := A262059val(lowk) ;
%p valhigh := A262059val(highk) ;
%p if valhigh > n and vallow <= n and highk= lowk+1 then
%p return highk;
%p else
%p midk := floor((lowk+highk)/2) ;
%p valmid := A262059val(midk) ;
%p if valmid < n then
%p return procname(n,midk,highk) ;
%p else
%p return procname(n,lowk,midk) ;
%p end if;
%p end if;
%p end proc:
%p A262059 := proc(n)
%p local lowk,highk,p ;
%p if n = 1 then
%p return 2;
%p end if;
%p for p from 0 do
%p lowk := 10^p ;
%p highk := 10^(p+1) ;
%p if A262059val(highk) >=n then
%p return A262059lims(n,min(2,lowk),highk) ;
%p end if;
%p end do:
%p end proc: # _R. J. Mathar_, Oct 22 2015
%t f[n_] := f[n] = Block[{k = f[n - 1]}, While[n > k^(1/3)/Log[k], k++]; k]; f[1] = 2; Array[f, 40]
%o (PARI) a(n) = {my(k = 2); while(sqrtn(k,3)/log(k) <= n, k++); k;} \\ _Michel Marcus_, Sep 10 2015
%Y Cf. A088346, A262058, A262060.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Sep 09 2015
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