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A201879
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Numbers n such that sigma_2(n) - n^2 is a square.
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1
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1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 61, 67, 70, 71, 73, 79, 83, 89, 97, 101, 102, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257
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internal format)
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OFFSET
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1,2
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COMMENTS
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Numbers n such that sum of the square of proper (or aliquot) divisors of n is a square.
All primes are in this sequence. Nonprimes in the sequence are 1, 30, 70, 102, 282, 286, 646, 730, 920, 1242, ... - Charles R Greathouse IV, Dec 06 2011
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LINKS
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FORMULA
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EXAMPLE
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a(12)=30 because the aliquot divisors of 30 are 1, 2, 3, 5, 6, 10, 15, the sum of whose squares is 1^2 + 2^2 + 3^2 + 5^2 + 6^2 + 10^2 + 15^2 = 400 = 20^2.
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MAPLE
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numtheory[sigma][2](n)-n^2 ;
end proc:
isA201879 := proc(n)
end proc:
for n from 1 to 300 do
if isA201879(n) then
printf("%d, ", n);
end if;
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MATHEMATICA
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Select[Range[400], IntegerQ[Sqrt[DivisorSigma[2, #]-#^2]]&]
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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