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 A064180 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. 0
 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; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE 117 is in the sequence because the divisors of 117 are 1, 3, 9, 13, 39 and 117. Being squarefree 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. MATHEMATICA Select[ Range[2, 25000], IntegerQ[ Sqrt[ Apply[ Plus, Delete[ Divisors[ # ], -1]] - 1]] && IntegerQ[ Sqrt[ Apply[ Times, Delete[ Divisors[ # ], -1]]]] && ! PrimeQ[ # ] & ] CROSSREFS Sequence in context: A201021 A187990 A112877 * A050245 A031174 A146172 Adjacent sequences:  A064177 A064178 A064179 * A064181 A064182 A064183 KEYWORD easy,nonn AUTHOR Robert G. Wilson v, Oct 14 2001 STATUS approved

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