A341676 - OEIS

%I #14 Nov 01 2024 05:16:48

%S 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 13,41,7,43,11,23,47,7,17,13,53,11,19,29,59,61,31,13,11,67,17,23,71,

%U 73,37,19,11,13,79,41,83,17,43,29,11,89,13,23,31,47,19

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

%C 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 Amiram Eldar, <a href="/A341676/b341676.txt">Table of n, a(n) for n = 1..10000</a>

%e The sequence of superior prime divisors begins: {}, {2}, {3}, {2}, {5}, {3}, {7}, {}, {3}, {5}, {11}, {}, {13}, {7}, {5}, {}, {17}, {}, {19}, {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 Inferior versions are A107286 (smallest), A217581 (largest), A056608.

%Y These divisors (superior prime) are counted by A341591.

%Y The strictly superior version is A341643.

%Y A001221 counts prime divisors, with sum A001414.

%Y A033676 selects the greatest inferior divisor.

%Y A033677 selects the smallest superior divisor.

%Y A038548 counts superior (or inferior) divisors.

%Y A056924 counts strictly superior (or strictly inferior) divisors.

%Y A060775 selects the greatest strictly inferior divisor.

%Y A063538/A063539 have/lack a superior prime divisor.

%Y A070038 adds up superior divisors.

%Y A140271 selects the smallest strictly superior divisor.

%Y A161908 lists superior divisors.

%Y A207375 lists central divisors.

%Y - Inferior: A063962, A066839, A069288, A161906, A333749, A333750.

%Y - Superior: A051283, A059172, A063539, A070038, A116882, A341592, A341593.

%Y - Strictly Inferior: A070039, A333805, A333806, A341596, A341674, A341677.

%Y - Strictly Superior: A048098, A064052, A238535, A341594, A341595, A341642, A341643, A341644, A341645, A341646, A341673.

%Y Cf. A000005, A000203, A001222, A001248, A006530, A020639, A112798.

%K nonn

%O 1,1

%A _Gus Wiseman_, Feb 23 2021