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Search: id:A063717
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| A063717 |
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Greatest divisor of n^2 that is less than n. |
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3
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| 1, 1, 2, 1, 4, 1, 4, 3, 5, 1, 9, 1, 7, 9, 8, 1, 12, 1, 16, 9, 11, 1, 18, 5, 13, 9, 16, 1, 25, 1, 16, 11, 17, 25, 27, 1, 19, 13, 32, 1, 36, 1, 22, 27, 23, 1, 36, 7, 25, 17, 26, 1, 36, 25, 49, 19, 29, 1, 50, 1, 31, 49, 32, 25, 44, 1, 34, 23, 50, 1, 64, 1, 37, 45, 38, 49, 52, 1, 64, 27, 41
(list; graph; listen)
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OFFSET
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2,3
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COMMENT
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Smaller of two distinct numbers with minimum sum whose geometric mean is n. E.g. a(12) = 9 as 12^2 = 144 = 1*144= 2*72 = 3*48 = 4*36=6*24=8*18=9*16 etc. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 15 2003
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EXAMPLE
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a(45)=27 because set of divisors of 45^2 is {1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025} and the greatest element of the set less than 45 is 27.
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MAPLE
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with(numtheory): for n from 2 to 200 do a := divisors(n^2): b := a[(tau(n^2)-1)/2]: printf(`%d, `, b); od:
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MATHEMATICA
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f[n_] := Module[{dn2 = Divisors[n^2]}, Last[Take[dn2, {1, Flatten[Position[dn2, n]][[ 1]] - 1}]]]; Table[f[i], {i, 2, 85}]
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CROSSREFS
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A063649(n)=n+a(n), A063718(n)=n^2/A063717(n), A063428(n)=n-a(n).
Cf. A063718.
Sequence in context: A035092 A107457 A112350 this_sequence A024994 A051953 A079277
Adjacent sequences: A063714 A063715 A063716 this_sequence A063718 A063719 A063720
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 12 2001
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