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A140271
Least divisor of n that is > sqrt(n), with a(1) = 1.
36
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
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
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
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.
- Strictly Inferior: A070039, A333805, A333806, A341596, A341677.
- Strictly Superior: A048098, A064052, A341643, A341644, A341646.
Sequence in context: A088491 A353172 A392843 * A223491 A346088 A275823
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