A154585 a(n) = abs(Sum_{k=1..n} (-1)^k * (n-k+1 mod k)).

0, 1, 1, 0, 1, 2, 4, 0, 3, 4, 5, 4, 1, 10, 4, 3, 1, 2, 9, 2, 11, 12, 17, 11, 0, 13, 0, 1, 6, 7, 23, 8, 7, 20, 10, 9, 8, 25, 14, 13, 4, 3, 20, 13, 34, 35, 34, 26, 8, 13, 6, 5, 8, 25, 24, 1, 26, 27, 34, 33, 4, 37, 25, 6, 11, 12, 11, 16, 37, 38, 60, 59, 24, 25, 0, 19, 40, 41, 54, 14, 25, 26, 51

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jan 12 2009

Keywords

• easy
• nonn

Examples

			a(5) = -(5 mod 1)+(4 mod 2)-(3 mod 3)+(2 mod 4)-(1 mod 5) = -0+0-0+2-1 = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004125, A051127, A154586.

Programs

Maple

P:=proc(i) local a,n; for n from 1 by 1 to i do a:=abs(sum('(-1)^k*((n-k+1) mod k)','k'=1..n)); print(a); od; end: P(100);

Mathematica

a[n_] := Abs @ Sum[(-1)^k * Mod[n - k + 1, k], {k, 1, n}]; Array[a, 100] (* Amiram Eldar, Sep 18 2021 *)

PARI

a(n) = abs(sum(k=1, n, (-1)^k * lift(Mod(n-k+1, k)))); \\ Michel Marcus, Sep 18 2021