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A046762
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Sum of the squares of the divisors of n is divisible by n.
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5
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1, 10, 60, 65, 84, 130, 140, 150, 175, 260, 350, 420, 525, 780, 1050, 1105, 1820, 2100, 2210, 4420, 4650, 5425, 5460, 8840, 10500, 10850, 13260, 16275, 19720, 20150, 20737, 21700, 30225, 30940, 32045, 32550, 41474, 45500, 55250, 57350, 60450
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Compare with multiply perfect numbers A007691. Here Sum[ divisors ] is replaced by Sum[ square 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
| Florian Luca, Problem 11090: Sometimes n divides sigma_k(n), Amer. Math. Monthly 113 (2006), 372-373.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
| n=65=a[ 4 ], sigma[ 2,65 ]=4420=65*68=68*n or n=1820=a[ 17 ], the divisor-square sum is 4641000=2550*1820=2880*n
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MATHEMATICA
| Select[Range[70000], Divisible[DivisorSigma[2, #], #]&] [From Harvey P. Dale, Dec. 15, 2010]
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CROSSREFS
| A007691.
Sequence in context: A054489 A140890 A055714 * A066290 A065641 A121874
Adjacent sequences: A046759 A046760 A046761 * A046763 A046764 A046765
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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