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A341676 The unique superior prime divisor of each number that has one.

%I A341676 #14 Nov 01 2024 05:16:48
%S A341676 2,3,2,5,3,7,3,5,11,13,7,5,17,19,5,7,11,23,5,13,7,29,31,11,17,7,37,19,
%T A341676 13,41,7,43,11,23,47,7,17,13,53,11,19,29,59,61,31,13,11,67,17,23,71,
%U A341676 73,37,19,11,13,79,41,83,17,43,29,11,89,13,23,31,47,19
%N A341676 The unique superior prime divisor of each number that has one.
%C A341676 We define a divisor d|n to be superior if d >= n/d. Superior divisors are counted by A038548 and listed by A161908. Numbers with a superior prime divisor are listed by A063538.
%H A341676 Amiram Eldar, <a href="/A341676/b341676.txt">Table of n, a(n) for n = 1..10000</a>
%e A341676 The sequence of superior prime divisors begins: {}, {2}, {3}, {2}, {5}, {3}, {7}, {}, {3}, {5}, {11}, {}, {13}, {7}, {5}, {}, {17}, {}, {19}, {5}, ...
%t A341676 Join@@Table[Select[Divisors[n],PrimeQ[#]&&#>=n/#&],{n,100}]
%o A341676 (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 A341676 Inferior versions are A107286 (smallest), A217581 (largest), A056608.
%Y A341676 These divisors (superior prime) are counted by A341591.
%Y A341676 The strictly superior version is A341643.
%Y A341676 A001221 counts prime divisors, with sum A001414.
%Y A341676 A033676 selects the greatest inferior divisor.
%Y A341676 A033677 selects the smallest superior divisor.
%Y A341676 A038548 counts superior (or inferior) divisors.
%Y A341676 A056924 counts strictly superior (or strictly inferior) divisors.
%Y A341676 A060775 selects the greatest strictly inferior divisor.
%Y A341676 A063538/A063539 have/lack a superior prime divisor.
%Y A341676 A070038 adds up superior divisors.
%Y A341676 A140271 selects the smallest strictly superior divisor.
%Y A341676 A161908 lists superior divisors.
%Y A341676 A207375 lists central divisors.
%Y A341676 - Inferior: A063962, A066839, A069288, A161906, A333749, A333750.
%Y A341676 - Superior: A051283, A059172, A063539, A070038, A116882, A341592, A341593.
%Y A341676 - Strictly Inferior: A070039, A333805, A333806, A341596, A341674, A341677.
%Y A341676 - Strictly Superior: A048098, A064052, A238535, A341594, A341595, A341642, A341643, A341644, A341645, A341646, A341673.
%Y A341676 Cf. A000005, A000203, A001222, A001248, A006530, A020639, A112798.
%K A341676 nonn
%O A341676 1,1
%A A341676 _Gus Wiseman_, Feb 23 2021