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Search: id:A064180
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| A064180 |
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The sum of the proper divisors of n not including 1, Chowla'a function (A048050) and the product of the proper divisors or aliquot parts of n (A007956) are both perfect squares. |
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+0
1
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| 117, 208, 292, 320, 475, 539, 549, 567, 873, 964, 1737, 2107, 2692, 2997, 3573, 3904, 4477, 4802, 5275, 5284, 5968, 6057, 7267, 7488, 7492, 9189, 9457, 9475, 10084, 10377, 11072, 11728, 11737, 12717, 13769, 14373, 14692, 16219, 16399, 17397
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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117 is in the sequence because the divisors of 117 are 1, 3, 9, 13, 39 and 117. Being square-free itself, the product of divisors is a perfect square. The sum of the divisors in question, 3+9+13+39 = 64 and it is a perfect square.
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MATHEMATICA
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Select[ Range[2, 25000], IntegerQ[ Sqrt[ Apply[ Plus, Delete[ Divisors[ # ], -1]] - 1]] && IntegerQ[ Sqrt[ Apply[ Times, Delete[ Divisors[ # ], -1]]]] && ! PrimeQ[ # ] & ]
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CROSSREFS
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Sequence in context: A095625 A109023 A112877 this_sequence A050245 A031174 A146172
Adjacent sequences: A064177 A064178 A064179 this_sequence A064181 A064182 A064183
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KEYWORD
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easy,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 14 2001
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