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A046520
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a(n) = (sum of divisors of n) - phi(n) - (number of divisors of n).
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3
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-1, 0, 0, 2, 0, 6, 0, 7, 4, 10, 0, 18, 0, 14, 12, 18, 0, 27, 0, 28, 16, 22, 0, 44, 8, 26, 18, 38, 0, 56, 0, 41, 24, 34, 20, 70, 0, 38, 28, 66, 0, 76, 0, 58, 48, 46, 0, 98, 12, 67, 36, 68, 0, 94, 28, 88, 40, 58, 0, 140, 0, 62, 62, 88, 32, 116, 0, 88, 48, 112, 0, 159, 0, 74
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OFFSET
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1,4
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COMMENTS
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Always >= 0 for n >= 2. a(n)=0 if and only if n is prime.
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REFERENCES
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József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter I, p. 10, section I.3.1.a (but they have "tau" instead of "sigma").
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LINKS
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FORMULA
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MAPLE
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MATHEMATICA
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DivisorSigma[1, #] - EulerPhi[#] - DivisorSigma[0, #] & /@ Range[74] (* Jayanta Basu, Jun 27 2013 *)
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PROG
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(PARI) a(n) = {my(f = factor(n)); sigma(f) - eulerphi(f) - numdiv(f); } \\ Amiram Eldar, Apr 25 2024
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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