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Search: id:A046763
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| A046763 |
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Numbers n such that the sum of the cubes of the divisors of n is divisible by n. |
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+0
5
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| 1, 6, 42, 120, 168, 270, 280, 312, 496, 672, 728, 840, 1080, 1560, 1782, 1806, 1890, 2044, 2184, 2520, 3472, 3640, 3913, 4256, 5880, 6048, 6552, 6615, 7224, 7560, 7826, 8128, 9120, 9424, 9933, 10804, 10920, 11400, 12040, 12768, 13230, 13626, 14040
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OFFSET
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1,2
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COMMENT
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Compare with multiply perfect numbers, A007691. Here Sum[ divisors ] is replaced by Sum[ cube of divisors ].
Problem 11090 proves that this sequence is infinite. - T. D. Noe (noe(AT)sspectra.com), Apr 18 2006
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REFERENCES
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Florian Luca, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113 (2006), 372-373.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
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n = 168 = a[ 5 ], Sum[ d^3 ] = 5634720 = 33540*168 = 33540*n or if n = 8128, Sigma[ 3,8128 ] = 613681507712 = 8128*75502154. Moreover 8128 is a perfect number.
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CROSSREFS
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Cf. A007691.
Sequence in context: A153786 A164016 A147811 this_sequence A082986 A062136 A047663
Adjacent sequences: A046760 A046761 A046762 this_sequence A046764 A046765 A046766
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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