A079529 a(n) = sigma(n) - ceiling(n + sqrt n) as n runs through the composite numbers A002808.

1, 3, 4, 1, 4, 12, 6, 5, 11, 16, 17, 6, 9, 31, 1, 10, 7, 22, 36, 25, 9, 14, 7, 49, 15, 10, 43, 47, 33, 26, 19, 69, 1, 35, 13, 38, 58, 9, 56, 15, 24, 100, 26, 33, 55, 10, 69, 49, 18, 65, 114, 31, 40, 55, 10, 81, 97, 31, 34, 130, 13, 36, 23, 82, 134, 11, 66, 25, 40, 15, 146, 63, 47, 107

Offset

1,2

Comments

It is known that a(n) >= 0.

References

József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 77, section III.1.1.a.

Wacław Sierpiński, Elementary Theory of Numbers. Państ. Wydaw. Nauk., Warsaw, 1964.

Links

Table of n, a(n) for n=1..74.

Wacław Sierpiński, Elementary Theory of Numbers, Warszawa, 1964.

Mathematica

s[n_] := If[CompositeQ[n], DivisorSigma[1, n] - Ceiling[n + Sqrt[n]], Nothing]; Array[s, 100] (* Amiram Eldar, Apr 25 2024 *)

Prog

(PARI) lista(nn) = forcomposite(n=1, nn, print1(sigma(n) - ceil(n + sqrt(n)), ", ")); \\ Michel Marcus, Dec 12 2014
(Python)
from math import isqrt
from sympy import divisor_sigma, composite
def A079529(n): return divisor_sigma(m:=composite(n))-1-m-isqrt(m-1) # Chai Wah Wu, Jul 29 2022

Crossrefs

Cf. A000203, A002808, A079528, A055682, A058208.

Sequence in context: A299446 A300084 A321624 * A361508 A299022 A298532

Adjacent sequences: A079526 A079527 A079528 * A079530 A079531 A079532

Keyword

nonn

Author

N. J. A. Sloane, Jan 22 2003

Status

approved