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A238535
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Sum of divisors d of n where d > sqrt(n).
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35
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0, 2, 3, 4, 5, 9, 7, 12, 9, 15, 11, 22, 13, 21, 20, 24, 17, 33, 19, 35, 28, 33, 23, 50, 25, 39, 36, 49, 29, 61, 31, 56, 44, 51, 42, 75, 37, 57, 52, 78, 41, 84, 43, 77, 69, 69, 47, 108, 49, 85, 68, 91, 53, 108, 66, 106, 76, 87, 59, 147, 61, 93, 93, 112, 78, 132
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OFFSET
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1,2
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COMMENTS
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Properties of the sequence:
a(n) = n if n is prime because sigma(n) = n+1 and A066839(n) = 1;
a(p^2) = p^2 if p is prime because sigma(p^2) = p^2+p+1 and A066839(p^2)= p+1 => A000203(p^2) - A066839(p^2)= p^2;
a(m) = 2*m if m = A182147(n) = 42, 54, 66, 78, 102, 114,... (numbers n equal to the sum of its proper divisors greater than square root of n).
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LINKS
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FORMULA
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EXAMPLE
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MATHEMATICA
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lst={}; f[n_]:=DivisorSigma[1, n]-Plus@@Select[Divisors@n, #<=Sqrt@n&]; Do[If[IntegerQ[f[n]], AppendTo[lst, f[n]]], {n, 1, 200}]; lst
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PROG
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(PARI) a(n) = sumdiv(n, d, d*(d>sqrt(n))); \\ Michel Marcus, Feb 28 2014
(Sage)
def a(n):
return sum([d for d in Integer(n).divisors() if d>sqrt(n)]) # Ralf Stephan, Mar 08 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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