

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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..40.


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



