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A140271
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Least divisor of n that is > sqrt(n), with a(1) = 1.
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36
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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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)
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MAPLE
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with(numtheory):
a:= n-> min(select(d-> is(d=n or d>sqrt(n)), divisors(n))):
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MATHEMATICA
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PROG
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(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
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CROSSREFS
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These divisors are counted by A056924.
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.
A341674 lists strictly inferior divisors.
- Superior: A051283, A059172, A063538, A063539, A070038, A072500, A116882, A116883, A341591, A341592, A341593, A341675, A341676.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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