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Search: id:A056737
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| A056737 |
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Minimum nonnegative integer m such that n = k*(k+m) for some positive integer k. |
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+0
6
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| 0, 1, 2, 0, 4, 1, 6, 2, 0, 3, 10, 1, 12, 5, 2, 0, 16, 3, 18, 1, 4, 9, 22, 2, 0, 11, 6, 3, 28, 1, 30, 4, 8, 15, 2, 0, 36, 17, 10, 3, 40, 1, 42, 7, 4, 21, 46, 2, 0, 5, 14, 9, 52, 3, 6, 1, 16, 27, 58, 4, 60, 29, 2, 0, 8, 5, 66, 13, 20, 3, 70, 1, 72, 35, 10, 15, 4, 7, 78, 2, 0, 39, 82, 5, 12, 41
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) is difference between the least divisor of n that is >= square root(n) and the greatest divisor of n that is <= square root(n).
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FORMULA
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a(n) = Min{t - d | 0 < d <= t <= n and d*t=n}. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 25 2002
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EXAMPLE
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a(8) = 2 because 8 = 2*(2+2) and 8 = k*(k+1) or 8 = k^2 have no solutions for k = a positive integer.
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MATHEMATICA
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A033676[n_] := If[EvenQ[DivisorSigma[0, n]], Divisors[n][[DivisorSigma[0, n]/2]], Sqrt[n]] A033677[n_] := If[EvenQ[DivisorSigma[0, n]], Divisors[n][[DivisorSigma[0, n]/2+1]], Sqrt[n]] Table[A033677[n] - A033676[n], {n, 1, 128}] (Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 27 2004)
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CROSSREFS
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Sequence in context: A020781 A007432 A079124 this_sequence A008797 A109468 A081880
Adjacent sequences: A056734 A056735 A056736 this_sequence A056738 A056739 A056740
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Aug 26 2000
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