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A235796
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2*n - 1 - sigma(n).
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12
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0, 0, 1, 0, 3, -1, 5, 0, 4, 1, 9, -5, 11, 3, 5, 0, 15, -4, 17, -3, 9, 7, 21, -13, 18, 9, 13, -1, 27, -13, 29, 0, 17, 13, 21, -20, 35, 15, 21, -11, 39, -13, 41, 3, 11, 19, 45, -29, 40, 6, 29, 5, 51, -13, 37, -9, 33, 25, 57, -49, 59, 27, 21, 0, 45, -13, 65, 9, 41
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OFFSET
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1,5
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COMMENTS
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It appears that a(n) = 0 iff n is a power of 2.
Numbers n with a(n) = 0 are called "almost perfect", "least deficient" or "slightly defective" numbers. See A000079. - Robert Israel, Jul 22 2014
a(n) = n - 2 iff n is prime.
a(n) = -1 iff n is a perfect number.
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, New York, 2004.
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LINKS
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FORMULA
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EXAMPLE
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. The positive The sum of
n odd numbers divisors of n. a(n)
1 1 1 0
2 3 3 0
3 5 4 1
4 7 7 0
5 9 6 3
6 11 12 -1
7 13 8 5
8 15 15 0
9 17 13 4
10 19 18 1
...
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MATHEMATICA
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Table[2n-1-DivisorSigma[1, n], {n, 70}] (* Harvey P. Dale, Jul 11 2014 *)
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PROG
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(PARI) vector(100, n, (2*n-1)-sigma(n)) \\ Colin Barker, Jan 27 2014
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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