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%I #59 Apr 25 2024 13:55:58
%S 1,1,1,2,1,2,1,2,3,2,1,3,1,2,3,2,1,3,1,2,3,2,1,3,5,2,3,2,1,5,1,2,3,2,
%T 5,3,1,2,3,5,1,3,1,2,5,2,1,3,7,5,3,2,1,3,5,7,3,2,1,5,1,2,7,2,5,3,1,2,
%U 3,7,1,3,1,2,5,2,7,3,1,5,3,2,1,7,5,2,3
%N Largest prime divisor of n <= sqrt(n), 1 if n is prime or 1.
%C If we define a divisor d|n to be inferior if d <= n/d, then inferior divisors are counted by A038548 and listed by A161906. This sequence selects the greatest inferior prime divisor of n. - _Gus Wiseman_, Apr 06 2021
%H T. D. Noe, <a href="/A217581/b217581.txt">Table of n, a(n) for n = 1..10000</a>
%e From _Gus Wiseman_, Apr 06 2021: (Start)
%e The sequence selects the greatest element (or 1 if empty) of each of the following sets of strictly superior divisors:
%e 1:{} 16:{2} 31:{} 46:{2}
%e 2:{} 17:{} 32:{2} 47:{}
%e 3:{} 18:{2,3} 33:{3} 48:{2,3}
%e 4:{2} 19:{} 34:{2} 49:{7}
%e 5:{} 20:{2} 35:{5} 50:{2,5}
%e 6:{2} 21:{3} 36:{2,3} 51:{3}
%e 7:{} 22:{2} 37:{} 52:{2}
%e 8:{2} 23:{} 38:{2} 53:{}
%e 9:{3} 24:{2,3} 39:{3} 54:{2,3}
%e 10:{2} 25:{5} 40:{2,5} 55:{5}
%e 11:{} 26:{2} 41:{} 56:{2,7}
%e 12:{2,3} 27:{3} 42:{2,3} 57:{3}
%e 13:{} 28:{2} 43:{} 58:{2}
%e 14:{2} 29:{} 44:{2} 59:{}
%e 15:{3} 30:{2,3,5} 45:{3,5} 60:{2,3,5}
%e (End)
%p A217581 := n -> `if`(isprime(n) or n=1, 1, max(op(select(i->i^2<=n, numtheory[factorset](n)))));
%t Table[If[n == 1 || PrimeQ[n], 1, Select[Transpose[FactorInteger[n]][[1]], # <= Sqrt[n] &][[-1]]], {n, 100}] (* _T. D. Noe_, Mar 25 2013 *)
%o (PARI) a(n) = {my(m=1); foreach(factor(n)[,1], d, if(d^2 <= n, m=max(m,d))); m} \\ _Andrew Howroyd_, Oct 11 2023
%Y Cf. A033676.
%Y Positions of first appearances are 1 and A001248.
%Y These divisors are counted by A063962.
%Y These divisors add up to A097974.
%Y The smallest prime factor of the same type is A107286.
%Y A strictly superior version is A341643.
%Y A superior version is A341676.
%Y A038548 counts superior (or inferior) divisors.
%Y A048098 lists numbers without a strictly superior prime divisor.
%Y A056924 counts strictly superior (or strictly inferior) divisors.
%Y A063538/A063539 have/lack a superior prime divisor.
%Y A140271 selects the smallest strictly superior divisor.
%Y A161906 lists inferior divisors.
%Y A207375 lists central divisors.
%Y A341591 counts superior prime divisors.
%Y A341642 counts strictly superior prime divisors.
%Y A341673 lists strictly superior divisors.
%Y - Inferior: A066839, A069288, A333749, A333750.
%Y - Superior: A033677, A051283, A059172, A070038, A116882, A116883, A161908, A341592, A341593, A341675.
%Y - Strictly Inferior: A060775, A333805, A333806, A341596, A341674.
%Y - Strictly Superior: A238535, A341594, A341595, A341644, A341645, A341646.
%Y Cf. A000005, A001055, A001221, A001222, A001248, A001414, A006530, A020639, A064052.
%K nonn,changed
%O 1,4
%A _Peter Luschny_, Mar 21 2013
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