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A341643 The unique strictly superior prime divisor of each number that has one.

%I A341643 #11 Nov 01 2024 05:16:16
%S A341643 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 A341643 7,43,11,23,47,17,13,53,11,19,29,59,61,31,13,11,67,17,23,71,73,37,19,
%U A341643 11,13,79,41,83,17,43,29,11,89,13,23,31,47,19,97,11,101
%N A341643 The unique strictly superior prime divisor of each number that has one.
%C A341643 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 A341643 Amiram Eldar, <a href="/A341643/b341643.txt">Table of n, a(n) for n = 1..10000</a>
%e A341643 The strictly superior divisors of 15 are {5,15}, and A064052(10) = 15, so a(10) = 5.
%t A341643 Join@@Table[Select[Divisors[n],PrimeQ[#]&&#>n/#&],{n,100}]
%o A341643 (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 A341643 The inferior version is (largest inferior prime divisor) is A217581.
%Y A341643 These divisors (strictly superior prime) are counted by A341642.
%Y A341643 a(n) is the unique prime divisor in row n of A341673, for each n in A064052.
%Y A341643 The weak version is A341676.
%Y A341643 A038548 counts superior (or inferior) divisors.
%Y A341643 A048098 lists numbers without a strictly superior prime divisor.
%Y A341643 A056924 counts strictly superior (or strictly inferior) divisors.
%Y A341643 A063538/A063539 have/lack a superior prime divisors.
%Y A341643 A140271 selects the smallest strictly superior divisor.
%Y A341643 A207375 lists central divisors.
%Y A341643 A238535 adds up strictly superior divisors.
%Y A341643 A341591 counts superior prime divisors.
%Y A341643 - Inferior: A033676, A063962, A066839, A069288, A161906, A333749, A333750.
%Y A341643 - Superior: A033677, A051283, A059172, A070038, A116882, A116883, A161908, A341592, A341593, A341675.
%Y A341643 - Strictly Inferior: A060775, A333805, A333806, A341596, A341674.
%Y A341643 - Strictly Superior: A341594, A341595, A341644, A341645, A341646.
%Y A341643 Cf. A000005, A001055, A001221, A001248, A001414, A006530, A020639.
%K A341643 nonn
%O A341643 1,1
%A A341643 _Gus Wiseman_, Feb 20 2021