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A318879
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a(n) = Sum_{d|n} [d-(2*phi(d)) > 0]*(d-(2*phi(d))).
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8
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0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 6, 0, 2, 0, 0, 0, 8, 0, 6, 0, 2, 0, 14, 0, 2, 0, 6, 0, 18, 0, 0, 0, 2, 0, 24, 0, 2, 0, 14, 0, 22, 0, 6, 0, 2, 0, 30, 0, 12, 0, 6, 0, 26, 0, 14, 0, 2, 0, 54, 0, 2, 0, 0, 0, 30, 0, 6, 0, 26, 0, 56, 0, 2, 0, 6, 0, 34, 0, 30, 0, 2, 0, 66, 0, 2, 0, 14, 0, 66, 0, 6, 0, 2, 0, 62, 0, 16, 0, 36, 0, 42, 0, 14, 9
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OFFSET
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1,6
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LINKS
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FORMULA
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a(n) = -Sum_{d|n} [A083254(d) < 0]*A083254(d), where A083254(n) = 2*phi(n) - n, and [ ] are the Iverson brackets.
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EXAMPLE
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n = 105 has divisors [1, 3, 5, 7, 15, 21, 35, 105]. When A083254 is applied to them, we obtain [1, 1, 3, 5, 1, 3, 13, -9]. Summing the negative numbers present, and negating, we get a(105) = -(-9) = 9.
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PROG
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(PARI) A318879(n) = sumdiv(n, d, d=d-(2*eulerphi(d)); (d>0)*d);
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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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