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

1,6

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A004125, A051127, A154586.

Sequence in context: A004580 A215451 A375746 * A020822 A197514 A112635

Adjacent sequences: A154582 A154583 A154584 * A154586 A154587 A154588

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Jan 12 2009

Status

approved