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 A079528 a(n) = sigma(n) - ceiling(n + sqrt n). 2
 -1, -1, -1, 1, -2, 3, -2, 4, 1, 4, -3, 12, -3, 6, 5, 11, -4, 16, -4, 17, 6, 9, -4, 31, 1, 10, 7, 22, -5, 36, -5, 25, 9, 14, 7, 49, -6, 15, 10, 43, -6, 47, -6, 33, 26, 19, -6, 69, 1, 35, 13, 38, -7, 58, 9, 56, 15, 24, -7, 100, -7, 26, 33, 55, 10, 69, -8, 49, 18, 65, -8, 114, -8, 31, 40, 55, 10, 81, -8, 97 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS a(n) >= 0 if n composite. REFERENCES D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section III.1.1.a. W. Sierpiński, Elementary Theory of Numbers. Państ. Wydaw. Nauk., Warsaw, 1964. LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 W. Sierpiński, Elementary Theory of Numbers, Warszawa 1964. MATHEMATICA Table[DivisorSigma[1, n] -Ceiling[n +Sqrt[n]], {n, 1, 80}] (* G. C. Greubel, Jan 15 2019 *) PROG (PARI) vector(80, n, sigma(n) - ceil(n + sqrt(n))) \\ Michel Marcus, Dec 12 2014 (MAGMA) [SumOfDivisors(n)- Ceiling(n + Sqrt (n)): n in [1..100]]; // Vincenzo Librandi, Dec 13 2014 (Sage) [sigma(n, 1) - ceil(n+sqrt(n)) for n in (1..80)] # G. C. Greubel, Jan 15 2019 CROSSREFS Cf. A079529, A055682, A058208. Sequence in context: A181515 A183045 A060847 * A143422 A071438 A328169 Adjacent sequences:  A079525 A079526 A079527 * A079529 A079530 A079531 KEYWORD sign AUTHOR N. J. A. Sloane, Jan 22 2003 STATUS approved

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Last modified May 17 21:11 EDT 2021. Contains 343990 sequences. (Running on oeis4.)