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A158299
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Numerators of averages of squares of the divisors of n.
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1
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1, 5, 5, 7, 13, 25, 25, 85, 91, 65, 61, 35, 85, 125, 65, 341, 145, 455, 181, 91, 125, 305, 265, 425, 217, 425, 205, 175, 421, 325, 481, 455, 305, 725, 325, 637, 685, 905, 425, 1105, 841, 625, 925, 427, 1183, 1325, 1105, 341, 817, 1085, 725, 595, 1405, 1025
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Average of squares of the divisors of n = A001157(n)/A000005(n). Denominators of averages of squares of divisors of n: 1,2,1,1,1,4,1,4,3,4,1,1,1,4,1,5,1,6,1,1,. . ..
Because Mathematica represents rational numbers with the smallest possible denominator, the terms of the sequence are numerators appropriate to such denominators. For example, the divisors of 3 are 1 and 3, so their squares are 1 and 9. The mean of those squares could be represented as 10/2 or 5/1. Mathematica selects the latter so a(3) is 5 rather than 10. [From Harvey P. Dale, Oct 13 2011]
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 1..1000
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MATHEMATICA
| Numerator[Mean/@(Divisors[Range[60]]^2)] (* From Harvey P. Dale, Oct 13 2011 *)
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CROSSREFS
| Cf. A001157, A000005.
Sequence in context: A033300 A134130 A078551 * A093307 A141392 A088047
Adjacent sequences: A158296 A158297 A158298 * A158300 A158301 A158302
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KEYWORD
| nonn
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AUTHOR
| Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 15 2009
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EXTENSIONS
| Corrected and extended by Harvey P. Dale, Oct 13 2011
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