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%I #29 Apr 08 2021 08:23:13
%S 1,2,3,4,5,3,7,4,9,5,11,4,13,7,5,8,17,6,19,5,7,11,23,6,25,13,9,7,29,6,
%T 31,8,11,17,7,9,37,19,13,8,41,7,43,11,9,23,47,8,49,10,17,13,53,9,11,8,
%U 19,29,59,10,61,31,9,16,13,11,67,17,23,10,71,9,73,37,15,19,11,13,79,10,27
%N Least divisor of n that is > sqrt(n), with a(1) = 1.
%C If n is not a square, then a(n) = A033677(n).
%C If we define a divisor d|n to be strictly superior if d > n/d, then strictly superior divisors are counted by A056924 and listed by A341673. This sequence selects the smallest strictly superior divisor of n. - _Gus Wiseman_, Apr 06 2021
%H Alois P. Heinz, <a href="/A140271/b140271.txt">Table of n, a(n) for n = 1..10000</a>
%e From _Gus Wiseman_, Apr 06 2021: (Start)
%e a(n) is the smallest element in the following sets of strictly superior divisors:
%e 1: {1} 16: {8,16} 31: {31}
%e 2: {2} 17: {17} 32: {8,16,32}
%e 3: {3} 18: {6,9,18} 33: {11,33}
%e 4: {4} 19: {19} 34: {17,34}
%e 5: {5} 20: {5,10,20} 35: {7,35}
%e 6: {3,6} 21: {7,21} 36: {9,12,18,36}
%e 7: {7} 22: {11,22} 37: {37}
%e 8: {4,8} 23: {23} 38: {19,38}
%e 9: {9} 24: {6,8,12,24} 39: {13,39}
%e 10: {5,10} 25: {25} 40: {8,10,20,40}
%e 11: {11} 26: {13,26} 41: {41}
%e 12: {4,6,12} 27: {9,27} 42: {7,14,21,42}
%e 13: {13} 28: {7,14,28} 43: {43}
%e 14: {7,14} 29: {29} 44: {11,22,44}
%e 15: {5,15} 30: {6,10,15,30} 45: {9,15,45}
%e (End)
%p with(numtheory):
%p a:= n-> min(select(d-> is(d=n or d>sqrt(n)), divisors(n))):
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Jan 29 2018
%t Table[Select[Divisors[n], # > Sqrt[n] &][[1]], {n, 2, 70}] (* _Stefan Steinerberger_, May 18 2008 *)
%o (PARI) A140271(n)={local(d,a);d=divisors(n);a=n;for(i=1,length(d),if(d[i]>sqrt(n),a=min (d[i],a)));a} \\ _Michael B. Porter_, Apr 06 2010
%Y Cf. A060775, A033676, A033677.
%Y These divisors are counted by A056924.
%Y These divisors add up to A238535.
%Y These divisors that are odd are counted by A341594.
%Y These divisors that are squarefree are counted by A341595
%Y These divisors that are prime are counted by A341642.
%Y These divisors are listed by A341673.
%Y A038548 counts superior (or inferior) divisors.
%Y A161906 lists inferior divisors.
%Y A161908 lists superior divisors.
%Y A207375 list central divisors.
%Y A341674 lists strictly inferior divisors.
%Y - Inferior: A063962, A066839, A069288, A217581, A333749, A333750.
%Y - Superior: A051283, A059172, A063538, A063539, A070038, A072500, A116882, A116883, A341591, A341592, A341593, A341675, A341676.
%Y - Strictly Inferior: A070039, A333805, A333806, A341596, A341677.
%Y - Strictly Superior: A048098, A064052, A341643, A341644, A341646.
%Y Cf. A000005, A000203, A001221, A001222, A001248, A006530, A020639, A112798.
%K nonn
%O 1,2
%A _Leroy Quet_, May 16 2008
%E More terms from _Stefan Steinerberger_, May 18 2008
%E a(70)-a(80) from _Ray Chandler_, Jun 25 2009
%E _Franklin T. Adams-Watters_, Jan 26 2018, added a(1) = 1 to preserve the relation a(n) | n.
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