A166248 a(n) is the absolute value of n minus sum of all the remainders modulo the numbers below n.

1, 2, 2, 3, 1, 3, 1, 0, 3, 3, 11, 5, 15, 17, 21, 20, 34, 29, 45, 41, 49, 55, 75, 61, 78, 86, 98, 96, 122, 108, 136, 135, 151, 163, 183, 162, 196, 210, 230, 218, 256, 242, 282, 284, 294, 312, 356, 326, 365, 370, 398, 402, 452, 438, 474, 464, 496, 520, 576, 526, 584, 610

Offset

1,2

Links

Table of n, a(n) for n=1..62.

Formula

a(n) = abs(n - Sum_{k=1..n} (n mod k)).

a(n) = abs(n - A004125(n)). - Michel Marcus, May 08 2019

Example

a(1) = abs(1-0) = 1;
a(2) = abs(2-0) = 2;
a(3) = abs(3-1) = 2;
a(4) = abs(4-1) = 3;
a(5) = abs(5-4) = 1;
a(6) = abs(6-3) = 3;
a(7) = abs(7-8) = 1.

Maple

A004125 := proc(n) add( modp(n, k), k=1..n) ; end proc: A166248 := proc(n) abs(n-A004125(n)) ; end: seq(A166248(n), n=1..100) ; # R. J. Mathar, Oct 24 2009

Prog

(Python)
from math import isqrt
def A166248(n): return abs(n*(n-1)+((s:=isqrt(n))**2*(s+1)-sum((q:=n//k)*((k<<1)+q+1) for k in range(1, s+1))>>1)) # Chai Wah Wu, Nov 01 2023

Crossrefs

Cf. A000027, A004125, A163180.

Sequence in context: A200751 A077083 A274528 * A180257 A265576 A083040

Adjacent sequences: A166245 A166246 A166247 * A166249 A166250 A166251

Keyword

nonn

Author

Juri-Stepan Gerasimov, Oct 10 2009

Extensions

a(19), a(20), a(37) etc. corrected by R. J. Mathar, Oct 24 2009

Status

approved