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The unique strictly superior prime divisor of each number that has one.
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%I #11 Nov 01 2024 05:16:16

%S 2,3,5,3,7,5,11,13,7,5,17,19,5,7,11,23,13,7,29,31,11,17,7,37,19,13,41,

%T 7,43,11,23,47,17,13,53,11,19,29,59,61,31,13,11,67,17,23,71,73,37,19,

%U 11,13,79,41,83,17,43,29,11,89,13,23,31,47,19,97,11,101

%N The unique strictly superior prime divisor of each number that has one.

%C We define a divisor d|n to be strictly superior if d > n/d. Strictly superior divisors are counted by A056924 and listed by A341673.

%H Amiram Eldar, <a href="/A341643/b341643.txt">Table of n, a(n) for n = 1..10000</a>

%e The strictly superior divisors of 15 are {5,15}, and A064052(10) = 15, so a(10) = 5.

%t Join@@Table[Select[Divisors[n],PrimeQ[#]&&#>n/#&],{n,100}]

%o (PARI) lista(nmax) = {my(p); for(n = 1, nmax, p = select(x -> (x^2 > n), factor(n)[, 1]); if(#p == 1, print1(p[1], ", ")));} \\ _Amiram Eldar_, Nov 01 2024

%Y The inferior version is (largest inferior prime divisor) is A217581.

%Y These divisors (strictly superior prime) are counted by A341642.

%Y a(n) is the unique prime divisor in row n of A341673, for each n in A064052.

%Y The weak 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 divisors.

%Y A140271 selects the smallest strictly superior divisor.

%Y A207375 lists central divisors.

%Y A238535 adds up strictly superior divisors.

%Y A341591 counts superior prime divisors.

%Y - Inferior: A033676, A063962, A066839, A069288, A161906, 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: A341594, A341595, A341644, A341645, A341646.

%Y Cf. A000005, A001055, A001221, A001248, A001414, A006530, A020639.

%K nonn

%O 1,1

%A _Gus Wiseman_, Feb 20 2021