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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
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
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
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Jan 22 2003
STATUS
approved