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A140271 Least divisor of n that is > sqrt(n), with a(1) = 1.

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