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 A140271 Least divisor of n that is > sqrt(n), with a(1) = 1. 33
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If n is not a square, then a(n) = A033677(n). 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 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 EXAMPLE From Gus Wiseman, Apr 06 2021: (Start) a(n) is the smallest element in the following sets of strictly superior divisors:    1: {1}       16: {8,16}        31: {31}    2: {2}       17: {17}          32: {8,16,32}    3: {3}       18: {6,9,18}      33: {11,33}    4: {4}       19: {19}          34: {17,34}    5: {5}       20: {5,10,20}     35: {7,35}    6: {3,6}     21: {7,21}        36: {9,12,18,36}    7: {7}       22: {11,22}       37: {37}    8: {4,8}     23: {23}          38: {19,38}    9: {9}       24: {6,8,12,24}   39: {13,39}   10: {5,10}    25: {25}          40: {8,10,20,40}   11: {11}      26: {13,26}       41: {41}   12: {4,6,12}  27: {9,27}        42: {7,14,21,42}   13: {13}      28: {7,14,28}     43: {43}   14: {7,14}    29: {29}          44: {11,22,44}   15: {5,15}    30: {6,10,15,30}  45: {9,15,45} (End) MAPLE with(numtheory): a:= n-> min(select(d-> is(d=n or d>sqrt(n)), divisors(n))): seq(a(n), n=1..100);  # Alois P. Heinz, Jan 29 2018 MATHEMATICA Table[Select[Divisors[n], # > Sqrt[n] &][[1]], {n, 2, 70}] (* Stefan Steinerberger, May 18 2008 *) PROG (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 CROSSREFS Cf. A060775, A033676, A033677. These divisors are counted by A056924. These divisors add up to A238535. These divisors that are odd are counted by A341594. These divisors that are squarefree are counted by A341595 These divisors that are prime are counted by A341642. These divisors are listed by A341673. A038548 counts superior (or inferior) divisors. A161906 lists inferior divisors. A161908 lists superior divisors. A207375 list central divisors. A341674 lists strictly inferior divisors. - Inferior: A063962, A066839, A069288, A217581, A333749, A333750. - Superior: A051283, A059172, A063538, A063539, A070038, A072500, A116882, A116883, A341591, A341592, A341593, A341675, A341676. - Strictly Inferior: A070039, A333805, A333806, A341596, A341677. - Strictly Superior: A048098, A064052, A341643, A341644, A341646. Cf. A000005, A000203, A001221, A001222, A001248, A006530, A020639, A112798. Sequence in context: A002034 A248937 A088491 * A223491 A275823 A141295 Adjacent sequences:  A140268 A140269 A140270 * A140272 A140273 A140274 KEYWORD nonn AUTHOR Leroy Quet, May 16 2008 EXTENSIONS More terms from Stefan Steinerberger, May 18 2008 a(70)-a(80) from Ray Chandler, Jun 25 2009 Franklin T. Adams-Watters, Jan 26 2018, added a(1) = 1 to preserve the relation a(n) | n. STATUS approved

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Last modified May 5 19:29 EDT 2021. Contains 343573 sequences. (Running on oeis4.)