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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
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OFFSET
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1,2
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COMMENTS
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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, 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=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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MAPLE
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with(numtheory);
A046762:=proc(q)
local a, i, n;
for n from 1 to q do
a:=divisors(n); if frac(add(a[i]^2, i=1..nops(a))/n)=0 then print(n);
fi; od; end:
A046762(100000); # [Paolo P. Lava, Dec 07 2012]
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MATHEMATICA
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Select[Range[70000], Divisible[DivisorSigma[2, #], #]&] [From Harvey P. Dale, Dec 15 2010]
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PROG
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(PARI) is(n)=sigma(n, 2)%n==0 \\ Charles R Greathouse IV, Feb 04 2013
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CROSSREFS
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A007691.
Sequence in context: A213346 A140890 A055714 * A066290 A065641 A121874
Adjacent sequences: A046759 A046760 A046761 * A046763 A046764 A046765
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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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STATUS
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approved
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